10th Class Mathematics Introduction to Trigonometry Question Bank

done Trigonometry Total Questions - 40

• question_answer1)
  The value of \[\sin \theta \] in the adjoining figure is
  A)
  \[\frac{12}{5}\] done clear
  B)
  \[\frac{12}{13}\] done clear
  C)
  \[\frac{13}{12}\] done clear
  D)
  \[\frac{5}{12}\] done clear
  View Solution play_arrow

• question_answer2)
  In the given figure the value of \[\mathbf{cos}\phi \]is
  A)
  \[\frac{12}{5}\] done clear
  B)
  \[\frac{5}{12}\] done clear
  C)
  \[\frac{12}{5}\] done clear
  D)
  \[\frac{12}{13}\] done clear
  View Solution play_arrow

• question_answer3)
  In the given figure below, the value of \[\theta \] is
  A)
  \[{{60}^{{}^\circ }}\] done clear
  B)
  \[{{45}^{{}^\circ }}\] done clear
  C)
  \[{{90}^{{}^\circ }}\] done clear
  D)
  \[{{30}^{{}^\circ }}\] done clear
  View Solution play_arrow

• question_answer4)
  In the given figure below, what is the value of SQ?
  A)
  \[\frac{10}{\sqrt{3}}\]m done clear
  B)
  \[10\sqrt{3}\]m done clear
  C)
  \[\frac{20}{\sqrt{3}}\]m done clear
  D)
  30 m done clear
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• question_answer5)
  In the given figure below the value of AB is
  A)
  10.8                              done clear
  B)
  8.6 done clear
  C)
  6.8 done clear
  D)
  7.8 done clear
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• question_answer6)
  In the given figure \[\mathbf{BC}=\mathbf{CD}\]. Then, AB is equal to
  A)
  \[20\sqrt{3}\] done clear
  B)
  \[15\sqrt{3}\] done clear
  C)
  \[18\sqrt{2}\] done clear
  D)
  \[20\sqrt{2}\] done clear
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• question_answer7)
  In the adjoining figure the value of \[\mathbf{secl}{{\mathbf{7}}^{{}^\circ }}-\mathbf{sm7}{{\mathbf{3}}^{{}^\circ }}\]is
  A)
  \[\frac{y}{x\sqrt{{{y}^{2}}-{{x}^{2}}}}\] done clear
  B)
  \[\frac{{{x}^{2}}}{y\sqrt{{{y}^{2}}-{{x}^{2}}}}\] done clear
  C)
  \[\frac{{{x}^{2}}}{y\sqrt{{{x}^{2}}-{{y}^{2}}}}\] done clear
  D)
  \[\frac{{{y}^{2}}}{x\sqrt{{{x}^{2}}-{{y}^{2}}}}\] done clear
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• question_answer8)
  In the given right angles triangle XYZ. What is the value of \[\mathbf{secx}+\mathbf{tan}\text{ }\mathbf{x}\]?
  A)
  \[\frac{1}{\sqrt{6}}\] done clear
  B)
  \[\sqrt{6}\] done clear
  C)
  \[2\sqrt{6}\] done clear
  D)
  \[\frac{\sqrt{6}}{2}\] done clear
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• question_answer9)
  In the given figure, the value of \[\frac{1}{\cos e{{s}^{2}}}{{51}^{{}^\circ }}+{{\sin }^{2}}{{90}^{{}^\circ }}+{{\tan }^{2}}{{51}^{{}^\circ }}-\frac{1}{{{\sin }^{2}}{{51}^{{}^\circ }}{{\sec }^{2}}{{39}^{{}^\circ }}}\]is
  A)
  \[\sqrt{{{x}^{2}}-1}\] done clear
  B)
  \[\sqrt{1-{{x}^{2}}}\] done clear
  C)
  \[{{x}^{2}}-1\] done clear
  D)
  \[1-{{x}^{2}}\] done clear
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• question_answer10)
  In the adjoining figure, the value of CD is
  A)
  \[\frac{200}{3}\] done clear
  B)
  \[200\sqrt{3}\] done clear
  C)
  \[\frac{400}{3}\] done clear
  D)
  \[400\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer11)
  In the given figure what is the value of\[\tan \theta \]?
  A)
  \[\frac{p}{q}\] done clear
  B)
  \[\frac{q}{p}\] done clear
  C)
  pq done clear
  D)
  \[{{p}^{2}}{{q}^{2}}\] done clear
  View Solution play_arrow

• question_answer12)
  In the given figure the value of \[\frac{1+2\sin \theta .\cos \theta }{1-2\sin \theta .\cos \theta }\] is
  A)
  810 done clear
  B)
  540 done clear
  C)
  900 done clear
  D)
  490 done clear
  View Solution play_arrow

• question_answer13)
  In the given figure what is the value of \[\mathbf{3sin}\theta +\mathbf{4cos}\theta \]?
  A)
  3 done clear
  B)
  4 done clear
  C)
  5 done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer14)
  If \[sec\theta +tan\theta =x,(x\ne 0)\]then \[\mathbf{sec}\theta \]is equal to
  A)
  \[\left( x-\frac{1}{x} \right),x\ne 0\] done clear
  B)
  \[2\left( x-\frac{1}{x} \right),x\ne 0\] done clear
  C)
  \[\left( x+\frac{1}{x} \right),x\ne 0\] done clear
  D)
  \[\frac{1}{2}\left( x+\frac{1}{x} \right),x\ne 0\] done clear
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• question_answer15)
  If\[\mathbf{sin}\theta -\mathbf{cos}\theta =\sqrt{2}\mathbf{sin}\left( \mathbf{9}{{\mathbf{0}}^{{}^\circ }}-\theta  \right)\]then \[\mathbf{cot}\theta \]is equal to:
  A)
  \[\sqrt{2}\] done clear
  B)
  0 done clear
  C)
  \[\sqrt{2}-1\] done clear
  D)
  \[\sqrt{2}+1\] done clear
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• question_answer16)
  If \[se{{c}^{2}}\theta +ta{{n}^{2}}\theta =\sqrt{2}\], then the value of \[\left( \mathbf{se}{{\mathbf{c}}^{\mathbf{4}}}\theta -\mathbf{ta}{{\mathbf{n}}^{\mathbf{4}}}\theta  \right)\] is
  A)
  \[\frac{1}{\sqrt{3}}\] done clear
  B)
  1 done clear
  C)
  \[\sqrt{2}\] done clear
  D)
  0 done clear
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• question_answer17)
  If \[\mathbf{2}\beta \,\mathbf{sin}\theta =\alpha \,\mathbf{cos}\theta \] and \[\mathbf{2}\alpha \,\mathbf{cosec}\theta -\beta \,\mathbf{sec}\theta =\mathbf{3}\] then what is the value of\[\left( {{\alpha }^{\mathbf{2}}}+\mathbf{4}{{\beta }^{\mathbf{2}}} \right)\]?
  A)
  4 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  5 done clear
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• question_answer18)
  In the given figure \[\frac{2\tan \theta }{1-{{\tan }^{2}}\theta }\] is equal to
  A)
  \[\cos {{60}^{{}^\circ }}\] done clear
  B)
  \[\sin {{60}^{{}^\circ }}\] done clear
  C)
  \[\tan {{60}^{{}^\circ }}\] done clear
  D)
  \[\sin {{30}^{{}^\circ }}\] done clear
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• question_answer19)
  In the given figure \[\sin \theta =\]?
  A)
  \[\frac{m+n}{m-n}\] done clear
  B)
  \[\frac{m}{m+n}\] done clear
  C)
  \[\frac{m-n}{m+n}\] done clear
  D)
  \[\frac{n}{m+n}\] done clear
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• question_answer20)
  If \[\mathbf{sinA}=\frac{5}{13}\], then match the column.

  Column I		Column II
  A	Cos A	P	12/13
  B	Tan A	Q	5/12
  C	Cosec A	R	13/5
  D	Sec A	S	13/12

  A)
  (A-P, B-Q, C-R, D-S) done clear
  B)
  (A-Q, B-R, C-S, D-P) done clear
  C)
  (A-R, B-Q, C-S, D-P) done clear
  D)
  (A-P, B-Q, C-S, D-R) done clear
  View Solution play_arrow

• question_answer21)
  If cosec \[\mathbf{A}=\sqrt{\mathbf{5}}\]then match the column

  Column I		Column II
  A	Tan A	P	\[2/\sqrt{\mathbf{5}}\]
  B	Sin A	Q	\[\frac{3}{2}\]
  C	Cos A	R	\[\frac{1}{\sqrt{5}}\]
  D	\[\frac{1}{\tan A}+\frac{\sin A}{1+\cot A}\]	S	\[\frac{1}{2}\]

  A)
  (A-P, B-Q, C-R, D-S) done clear
  B)
  (A-S, B-R, C-P, D-Q) done clear
  C)
  (A-P, B-Q, C-S, D-R) done clear
  D)
  (A-P, B-S, C-Q, D-R) done clear
  View Solution play_arrow

• question_answer22)
  In the given figure the value of \[\mathbf{cot}\theta \]is
  A)
  \[\frac{2ab}{{{a}^{2}}-{{b}^{2}}}\] done clear
  B)
  \[\frac{2ab}{{{a}^{2}}+{{b}^{2}}}\] done clear
  C)
  \[\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\] done clear
  D)
  \[\frac{{{a}^{2}}+{{b}^{2}}}{2ab}\] done clear
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• question_answer23)
  Match the column

  Column I		Column II
  A	\[\cos ec({{90}^{{}^\circ }}-A)\]	P	Tan A
  B	\[\cot ({{90}^{{}^\circ }}-A)\]	Q	Sec A
  C	\[\tan ({{90}^{{}^\circ }}-A)\]	R	Cosec A
  D	\[\sec ({{90}^{{}^\circ }}-A)\]	S	Cot A

  A)
  (A-Q, B-P, C-S, D-R) done clear
  B)
  (A-P, B-Q, C-S, D-R) done clear
  C)
  (A-P, B-Q, C-R, D-S) done clear
  D)
  (A-R, B-S, C-P, D-Q) done clear
  View Solution play_arrow

• question_answer24)
  In given figure what is the value of \[\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}\theta -\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\theta \]?
  A)
  \[\frac{841}{41}\] done clear
  B)
  0 done clear
  C)
  1 done clear
  D)
  \[\frac{41}{841}\] done clear
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• question_answer25)
  In the given figure, \[\mathbf{PS}=\mathbf{SQ}\], then \[\mathbf{sin}\theta =\]?
  A)
  \[\frac{4{{Q}^{2}}-3{{p}^{2}}}{p}\] done clear
  B)
  \[\frac{p}{4{{Q}^{2}}-3{{p}^{2}}}\] done clear
  C)
  \[\frac{\sqrt{4{{Q}^{2}}-3{{p}^{2}}}}{p}\] done clear
  D)
  1 done clear
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• question_answer26)
  In the given figure, tan P. cot R =?
  A)
  1 done clear
  B)
  0 done clear
  C)
  \[\frac{25}{144}\] done clear
  D)
  \[\frac{144}{25}\] done clear
  View Solution play_arrow

• question_answer27)
  The value of \[\tan 4{}^\circ .\tan 43{}^\circ .\tan 47{}^\circ .\tan 86{}^\circ \]is
  A)
  2 done clear
  B)
  3 done clear
  C)
  1 done clear
  D)
  4 done clear
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• question_answer28)
  \[\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}{{\mathbf{6}}^{{}^\circ }}+\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}{{\mathbf{6}}^{{}^\circ }}+.......+\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{8}{{\mathbf{4}}^{{}^\circ }}+\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{8}{{\mathbf{5}}^{{}^\circ }}=\]?
  A)
  \[39\frac{1}{2}\] done clear
  B)
  \[40\frac{1}{2}\] done clear
  C)
  40 done clear
  D)
  \[49\frac{1}{\sqrt{2}}\] done clear
  View Solution play_arrow

• question_answer29)
  If \[\mathbf{tan}\alpha =\mathbf{ytan}\beta \] and \[\mathbf{sin}\alpha =\mathbf{xsin}\beta \], then \[\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}\alpha \] is
  A)
  \[\frac{{{x}^{2}}}{{{y}^{2}}+1}\] done clear
  B)
  \[\frac{{{x}^{2}}}{{{y}^{2}}}\] done clear
  C)
  \[\frac{{{x}^{2}}-1}{{{y}^{2}}-1}\] done clear
  D)
  \[\frac{{{x}^{2}}+1}{{{y}^{2}}+1}\] done clear
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• question_answer30)
  The product \[\mathbf{cos}\,{{\mathbf{1}}^{^{\mathbf{o}}}}\mathbf{cos}{{\mathbf{2}}^{\mathbf{o}}}\mathbf{cos}{{\mathbf{3}}^{\mathbf{o}}}\mathbf{cos}{{\mathbf{4}}^{\mathbf{o}}}.....\mathbf{cos18}{{\mathbf{0}}^{\mathbf{o}}}\]is equal to
  A)
  \[-1\] done clear
  B)
  \[\frac{1}{4}\] done clear
  C)
  1 done clear
  D)
  0 done clear
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• question_answer31)
  The simplified value of \[\left( \mathbf{secx}\,\mathbf{secy}+\mathbf{tanx}\,\mathbf{tany} \right)-\left( \mathbf{secx}\,\mathbf{tany}+\mathbf{tanx}\,\mathbf{secy} \right)\] is
  A)
  \[-1\] done clear
  B)
  0 done clear
  C)
  \[se{{c}^{2}}x\] done clear
  D)
  1 done clear
  View Solution play_arrow

• question_answer32)
  If \[\left( \mathbf{1}+\mathbf{sinx} \right)\left( \mathbf{l}+\mathbf{siny} \right)\left( \mathbf{l}+\mathbf{sinz} \right)\]\[=\left( \mathbf{l}-\mathbf{sinx} \right)\left( \mathbf{l}-\mathbf{siny} \right)\left( \mathbf{l}-\mathbf{sinz} \right)\] then each side is equal to
  A)
  \[\pm cosx\text{ }cosy\text{ }cosz\] done clear
  B)
  \[\pm \sin x\,\sin y\,sinz\] done clear
  C)
  \[\pm sinx\text{ }cosy\text{ }cosz\] done clear
  D)
  \[\pm \sin x\,siny\,cosz\] done clear
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• question_answer33)
  The numerical value of \[\frac{1}{1+{{\cot }^{2}}\theta }+\frac{4}{1+{{\tan }^{2}}\theta }+\mathbf{3si}{{\mathbf{n}}^{\mathbf{2}}}\theta \] will be
  A)
  2 done clear
  B)
  5 done clear
  C)
  6 done clear
  D)
  4 done clear
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• question_answer34)
  The value of \[\frac{\sin \theta }{1+\cos \theta }+\frac{\sin \theta }{1-{{\cos }^{2}}\theta }\] is\[\left( {{0}^{{}^\circ }}<\theta <{{90}^{{}^\circ }} \right)\]
  A)
  \[2\,cosec\theta \] done clear
  B)
  \[2\,sec\theta \] done clear
  C)
  \[2\,sin\theta \] done clear
  D)
  \[2\,cos\theta \] done clear
  View Solution play_arrow

• question_answer35)
  If \[\mathbf{x}=\mathbf{6}{{\mathbf{0}}^{{}^\circ }}\]then \[\frac{1}{2}\sqrt{1+cosx}+\frac{1}{2}\sqrt{1-cosx}\] is equal to
  A)
  \[cot\frac{\theta }{2}\] done clear
  B)
  \[\sec \frac{\theta }{2}\] done clear
  C)
  \[\sin \frac{\theta }{2}\] done clear
  D)
  \[\cos \frac{\theta }{2}\] done clear
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• question_answer36)
  If \[\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{x}=\mathbf{1}-{{\mathbf{e}}^{\mathbf{2}}}\], then the value of \[\mathbf{secx}+\mathbf{ta}{{\mathbf{n}}^{\mathbf{3}}}\mathbf{x}\text{ }\mathbf{cosecx}\] is
  A)
  \[{{(2+{{e}^{2}})}^{\frac{3}{2}}}\] done clear
  B)
  \[{{\left( 2-{{e}^{2}} \right)}^{\frac{1}{2}}}\] done clear
  C)
  \[{{\left( 2+{{e}^{2}} \right)}^{\frac{1}{2}}}\] done clear
  D)
  \[{{(2-{{e}^{2}})}^{\frac{3}{2}}}\] done clear
  View Solution play_arrow

• question_answer37)
  For any real values of \[\theta ,\frac{\sqrt{\sec \theta -1}}{\sqrt{\sec \theta +1}}=?\]
  A)
  \[cot\theta -cosec\theta \] done clear
  B)
  \[sec\theta -\tan \theta \] done clear
  C)
  \[cosec\theta +cot\theta \] done clear
  D)
  \[tan\theta -sec\theta \] done clear
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• question_answer38)
  Value of \[\frac{{{\sin }^{2}}\theta -2{{\sin }^{4}}\theta }{2{{\cos }^{4}}\theta -{{\cos }^{2}}\theta }-\mathbf{se}{{\mathbf{c}}^{\mathbf{2}}}\theta \] is
  A)
  1 done clear
  B)
  2 done clear
  C)
  -1 done clear
  D)
  0 done clear
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• question_answer39)
  If \[tan(x+y)=\sqrt{3}\] and \[\mathbf{tan}\left( \mathbf{x}-\mathbf{y} \right)=\frac{1}{\sqrt{3}},\]\[\angle \mathbf{x}+\angle \mathbf{y}<\mathbf{9}{{\mathbf{0}}^{{}^\circ }},\mathbf{x}\ge \mathbf{y},\] then \[\angle \mathbf{x}\]is
  A)
  \[{{90}^{{}^\circ }}\] done clear
  B)
  \[{{30}^{{}^\circ }}\] done clear
  C)
  \[{{45}^{{}^\circ }}\] done clear
  D)
  \[{{60}^{{}^\circ }}\] done clear
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• question_answer40)
  The value of \[\left( \mathbf{l}+\mathbf{sec4}{{\mathbf{0}}^{{}^\circ }}-\mathbf{cot5}{{\mathbf{0}}^{{}^\circ }} \right)\]\[\left( \mathbf{l}-\mathbf{cosec4}{{\mathbf{0}}^{{}^\circ }}+\mathbf{tan5}{{\mathbf{0}}^{{}^\circ }} \right)\] is equal to
  A)
  0 done clear
  B)
  1 done clear
  C)
  2 done clear
  D)
  -1 done clear
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