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

Question

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

(1) 1

(2) 0

(3) \(\frac{33}{65}\)

(4) \(\frac{32}{65}\)

Answer 1

Correct option is (2) 0  

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

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

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

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

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