Question

Assertion :${\sin }^{-1}\left(\sin \left(\frac{2\pi }{3}\right)\right)=\frac{\pi }{3}$ Reason: ${\sin }^{-1}\left(\sin \theta \right)=\theta ;$ where $\theta \in [-\frac{\pi }{2},\frac{\pi }{2}]$

• 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 incorrect but Reason is correct
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Clearly the reason is true as

${\sin }^{-1}\left(\sin \left(\frac{2\pi }{3}\right)\right)={\sin }^{-1}\left(\sin (\pi -\frac{\pi }{3})\right)={\sin }^{-1}\left(\sin \left(\frac{\pi }{3}\right)\right)=\frac{\pi }{3}$

$\Rightarrow$ Assertion is true and reason correctly explain the reason.