JEE Main & Advanced Mathematics Trigonometric Identities Question Bank

done Numerical Value Type Questions - Trigonometric Functions Total Questions - 15

• question_answer1)
  If for any \[\theta \in \left( \frac{\pi }{4},\frac{\pi }{2} \right)\] the expression \[3{{(\sin \theta -\cos \theta )}^{4}}+6{{(\sin \theta +\cos \theta )}^{2}}+4{{\sin }^{6}}\theta \] is equal to \[a-b\,\,{{\cos }^{6}}\theta ,\] then the value of \[\frac{a}{b}\] is
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• question_answer2)
  If \[0\le x<\frac{\pi }{2},\] then the number of values of x for which \[\sin x-\sin 2x+\sin 3x=0,\] is
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• question_answer3)
  If the value of \[\cos \frac{\pi }{{{2}^{2}}}.\cos \frac{\pi }{{{2}^{3}}}\cdot .....\cdot \cos \frac{\pi }{{{2}^{10}}}.\sin \frac{\pi }{{{2}^{10}}}={{2}^{\frac{1}{k}}},\] then k is equal to
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• question_answer4)
  If the maximum value of \[3\cos \theta +5\sin \left( \theta -\frac{\pi }{6} \right)\] for any real value of \[\theta \] is \[\sqrt{k},\] than k =
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• question_answer5)
  If \[si{{n}^{4}}\alpha +4{{\cos }^{4}}\beta +2=4\sqrt{2}\sin \alpha \cos \beta ;\]\[\alpha ,\beta \in [0,\pi ],\] and \[\cos (\alpha +\beta )-cos(\alpha -\beta )=-\sqrt{a},\] then a is
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• question_answer6)
  The value of \[{{\cos }^{2}}10{}^\circ -\cos 10{}^\circ \cos 50{}^\circ +{{\cos }^{2}}50{}^\circ \] is
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• question_answer7)
  The number of solutions of the equation \[1+{{\sin }^{4}}x={{\cos }^{2}}3x,\] \[x\in \left[ -\frac{5\pi }{2},\frac{5\pi }{2} \right]\] is
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• question_answer8)
  Let \[\alpha ,\beta \] be such that \[\pi <\alpha -\beta <3\pi \]. If \[\sin \alpha +\sin \beta =-\frac{21}{65}\] and \[\cos \alpha +\cos \beta =-\frac{27}{65}\] and if the value of \[\cos \frac{\alpha -\beta }{2}=\frac{-a}{\sqrt{b}},\] then \[a\times b=\]
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• question_answer9)
  A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length x. The maximum area (in sq. units) enclosed by the park is \[k{{x}^{2}},\] then k is equal to
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• question_answer10)
  If p and q are positive real numbers such that \[{{p}^{2}}+{{q}^{2}}=1,\] If the maximum value of \[(p+q)\] is equal to \[\sqrt{a}\] then a is equal to
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• question_answer11)
  The number of solutions of \[\tan x+\sec x=2\cos x\] in \[[0,\,2\pi )\] is
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• question_answer12)
  The number of values of x in the interval  \[[0,\,3\pi ]\]satisfying the equation \[2\text{ }si{{n}^{2}}x+5\text{ }sin\text{ x}-3=0\] is
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• question_answer13)
  If \[\cos \alpha +2\cos \beta +3\cos \gamma =0,\] \[\sin \alpha +2\sin \beta +3\sin \gamma =0\] and \[\alpha +\beta +\gamma =\pi ,\]then \[\sin 3\alpha +8\sin 3\beta +27sin3\gamma =\]
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• question_answer14)
  In triangle ABC given \[9{{a}^{2}}+9{{b}^{2}}-17{{c}^{2}}=0.\] If \[\frac{\cot A+\cot B}{\cot C}=\frac{m}{n},\] then the value of \[(m+n)\] equals
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• question_answer15)
  An observer on the top of a tree, finds the angle of depression of a car moving towards the tree to be \[30{}^\circ \]. After 3 minutes this angle becomes \[60{}^\circ \]. Then, the time in minutes after which the car will reach the tree is
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