cos (sin -1 3/5+sin -1 5/13+sin -1 33/65 ) is equal to :

Mathematics · Inverse Trigonometric Functions

JEE Main 2025 — 28 January, Morning Shift — Question 10

$\cos \left(\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{33}{65}\right)$ is equal to :

$\cos \left(\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{33}{65}\right)$

$\cos \left(\tan ^{-1} \frac{3}{4}+\tan ^{-1} \frac{5}{12}+\tan ^{-1} \frac{33}{56}\right)$

$\cos \left(\tan ^{-1}\left(\frac{\frac{3}{4}+\frac{5}{12}}{1-\frac{3}{4} \cdot \frac{5}{12}}\right)+\tan ^{-1} \frac{33}{56}\right)$

$\cos \left(\tan ^{-1} \frac{56}{33}+\cot ^{-1} \frac{56}{33}\right)$

$\cos \left(\frac{\pi}{2}\right)=0$

Answer key and solution verified before publishing.

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