Question

Assertion (A) : $si{n}^{-1}(sin5)=5$ (where $5$ is in radians)
Reason (R) : $si{n}^{-1}(sin\theta )=0$ for principal value.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Answer 1

Answer: (D)

$sin5=sin(\pi +\overline{5-\pi })$
$=-sin(5-\pi ),5-\pi \notin [-\frac{\pi }{2},\frac{\pi }{2}]=-sin(\pi +\overline{5-2\pi })$
$=sin(5-2\pi )$, where $5-2\pi \in [\frac{\pi }{2},\frac{\pi }{2}]$
$\therefore si{n}^{-1}(sin5)=si{n}^{-1}sin(5-2\pi )$
$\Rightarrow si{n}^{-1}(sin5)=5-2\pi \ne 5$
$\therefore$ Assertion (A) is false but given
Reason (R) is true.