Question

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

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

Answer 1

The correct option is C $4\pi -11$

${\cos }^{-1}\left(\cos \right(-5\left)\right)=-5+2\pi =a\text{(say)}$
${\sin }^{-1}\left(\sin 6\right)=6-2\pi =b\text{(say)}$
${\tan }^{-1}\left(\tan 12\right)=12-4\pi =c\text{(say)}$
$\therefore a+b-c=2\pi -5+6-2\pi -12+4\pi$
$=4\pi -11$