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.