Question

The value of $sin^{- 1} sin⁡17+cos^{- 1}⁡cos⁡10$ is equal to

• A. $27$
• B. $-27$
• C. $17-5\pi $
• D. $9\pi -27$

Answer 1

Answer: (D)

$\sin ^{-1} \sin 17=\sin ^{-1} \sin (17-5 \pi+5 \pi)$
$=5 \pi-17$
$\cos ^{-1}(\cos 10)=\cos ^{-1} \cos (10-3 \pi+3 \pi)$
$=\cos ^{-1} \cos \{3 \pi+(10-3 \pi)\}$
$=\cos ^{-1}\{-\cos (10-3 \pi)\}$
$=\pi-\cos ^{-1} \cos (10-3 \pi)$
$=\pi-(10-3 \pi)=4 \pi-10$
Hence, $\sin ^{-1} \sin 17+\cos ^{-1}(\cos 10)=9 \pi-27$