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question_answer1) If \[{{\sin }^{-1}}\sin 17+{{\cos }^{-1}}\cos 27+{{\tan }^{-1}}\tan 37\] is equal to \[k-\lambda \pi \] then find \[k+\lambda .\]
question_answer2) If the value of \[{{\cot }^{-1}}\frac{3}{4}+{{\sin }^{-1}}\frac{5}{13}\] is \[{{\sin }^{-1}}\left( \frac{a}{b} \right)\] then find \[b-a.\]
question_answer3) Find the value of \[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)+{{\sin }^{-1}}\left( \sin \frac{5\pi }{3} \right).\]
question_answer4) If \[\sum\limits_{i=1}^{20}{{{\sin }^{-1}}\,{{x}_{i}}=10\pi }\] then find the value of \[\sum\limits_{i=1}^{20}{{{x}_{i}}.}\]
question_answer5) If \[{{\sin }^{-1}}x+{{\sin }^{-1}}y+{{\sin }^{-1}}z=\frac{3\pi }{2},\]then find value of \[{{\cos }^{-1}}x+{{\cos }^{-1}}y+{{\cos }^{-1}}z.\]
question_answer6) If \[{{\left( {{\tan }^{-1}}x \right)}^{2}}+{{\left( {{\cot }^{-1}}x \right)}^{2}}=\frac{5{{\pi }^{2}}}{8},\]then find value of x.
question_answer7) If \[{{\cos }^{-1}}\left( \frac{15}{17} \right)+2{{\tan }^{-1}}\left( \frac{1}{5} \right)={{\cos }^{-1}}\left( \frac{140}{k} \right)\]then find k.
question_answer8) If \[{{\tan }^{-1}}x+2\,\,{{\cot }^{-1}}x=\frac{2\pi }{3},\]then find value of x.
question_answer9) If \[{{\sin }^{-1}}\frac{5}{x}+{{\sin }^{-1}}\frac{12}{x}=\frac{\pi }{2},\]then find value of x.
question_answer10) If \[{{\tan }^{-1}}\frac{x}{\pi }<\frac{\pi }{3},\,\,x\in \,N,\] then find the maximum value of x.
question_answer11) If \[2{{\sin }^{-1}}x={{\sin }^{-1}}\left( 2x\sqrt{1-{{x}^{2}}} \right)\] and \[\left| x \right|\,\,\le \,\,a\] then find a.
question_answer12) If the value of \[\sin \left( {{\cos }^{-1}}x \right)\] is \[\sqrt{1-{{x}^{n}}}\] then find value of n.
question_answer13) If \[{{\cos }^{-1}}p+{{\cos }^{-1}}q+{{\cos }^{-1}}\,\,r=\pi ,\] then find value of \[{{p}^{2}}+{{q}^{2}}+{{r}^{2}}+2pqr.\]
question_answer14) If the value of \[\cot \left( \text{cose}{{\text{c}}^{-1}}\frac{5}{3}+{{\tan }^{-1}}\frac{2}{3} \right)\] is \[\frac{k}{17}\] then find k.
question_answer15) Find the value of \[{{\cot }^{-1}}\frac{xy+1}{x-y}+{{\cot }^{-1}}\frac{yz+1}{y-z}+{{\cot }^{-1}}\frac{xz+1}{x-z}.\]
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