JEE Main 2019Inverse Trigonometric FunctionsInverse Trigonometric FunctionsMediumQuestioncos(sin−135+sin−1513+sin−13365)\cos \left(\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{33}{65}\right)cos(sin−153+sin−1135+sin−16533) is equal to:OptionsA3365\frac{33}{65}6533B1C3265\frac{32}{65}6532D0Check AnswerHide SolutionSolutioncos(sin−135+sin−1513+sin−13365)cos(tan−134+tan−1512+tan−13356)cos(tan−1(34+5121+34⋅512)+tan−13356)cos(tan−15633+cot−15633)cos(π2)=0\begin{aligned} & \cos \left(\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{33}{65}\right) \\ & \cos \left(\tan ^{-1} \frac{3}{4}+\tan ^{-1} \frac{5}{12}+\tan ^{-1} \frac{33}{56}\right) \\ & \cos \left(\tan ^{-1}\left(\frac{\frac{3}{4}+\frac{5}{12}}{1+\frac{3}{4} \cdot \frac{5}{12}}\right)+\tan ^{-1} \frac{33}{56}\right) \\ & \cos \left(\tan ^{-1} \frac{56}{33}+\cot ^{-1} \frac{56}{33}\right) \\ & \cos \left(\frac{\pi}{2}\right)=0 \end{aligned}cos(sin−153+sin−1135+sin−16533)cos(tan−143+tan−1125+tan−15633)cos(tan−1(1+43⋅12543+125)+tan−15633)cos(tan−13356+cot−13356)cos(2π)=0