( ^ -1 3 5 + ^ -1 5 13 + ^ -1 33 65 ) is equal to : - Vidyadip

MCQ

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

A
1
✓
0
C
$\frac{33}{65}$
D
$\frac{32}{65}$

✓

Answer

Correct option: B.

0

(B)
Sol. $\cos \left(\sin ^{-1} \frac{3}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{33}{65}\right)$
$\cos \left(\tan ^{-1} \frac{3}{4}+\tan ^{-1} \frac{5}{12}+\tan ^{-1} \frac{33}{56}\right)$
$\cos \left(\tan ^{-1}\left(\frac{\frac{3}{4}+\frac{5}{12}}{1+\frac{3}{4} \cdot \frac{5}{12}}\right)+\tan ^{-1} \frac{33}{56}\right)$
$\cos \left(\tan ^{-1} \frac{56}{33}+\cot ^{-1} \frac{56}{33}\right)$
$\cos \left(\frac{\pi}{2}\right)=0$

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