Question

Assertion :${\sin }^{-1}\left(\sin 5\right)=5$ (where 5 is in radians). Reason: ${\sin }^{-1}\left(\sin \theta \right)=\theta$ for principle value.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion false but Reason is true

Answer 1

The correct option is D Assertion false but Reason is true

${\sin }^{-1}\left(\sin 5\right)={\sin }^{-1}\left(\sin (5-2\pi )\right)=(5-2\pi )$

As $(5-2\pi )\in [-\frac{\pi }{2},\frac{\pi }{2}]$

Assertion false but Reason is true