Question

$\cos ^{-1}(\cos (-5))+\sin ^{-1}(\sin (6))-\tan ^{-1}(\tan (12))$ is equal to :
(The inverse trigonometric functions take the principal values)

• A. $3 \pi-11$
• B. $4 \pi-9$
• C. $4 \pi-11$
• D. $3 \pi+1$

Answer 1

Answer: (C)

$\cos ^{-1}(\cos (-5))+\sin ^{-1}(\sin (6))-\tan ^{-1}(\tan (12))$
$\Rightarrow (2 \pi-5)+(6-2 \pi)-(12-4 \pi)$
$\Rightarrow 4 \pi-11$