Question

Assertion: The value of $\sin \left[{\tan }^{-1}(-\sqrt{3})+{\cos }^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right]$ is $1$
Reason: ${\tan }^{-1}(-x)=\tan x$ and ${\cos }^{-1}(-x)={\cos }^{-1}x$

• A. Assertion is correct, reason is correct; reason is a correct explanation for assertion.
• B. Assertion is correct, reason is correct; reason is not a correct explanation for assertion
• C. Assertion is correct, reason is incorrect
• D. Assertion is incorrect, reason is correct.

Answer 1

Answer: (C)

$\sin \left[{\tan }^{-1}(-\sqrt{3})+{\cos }^{-1}\left(\frac{-\sqrt{3}}{2}\right)\right]$
$=\sin \left[-{\tan }^{-1}\sqrt{3}+\pi -{\cos }^{-1}\frac{\sqrt{3}}{2}\right]$
$=\sin \left[-\frac{\pi }{3}+\pi -\frac{\pi }{6}\right]=\sin \frac{\pi }{2}=1$
Hence, Assertion is correct but Reason is incorrect.