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The principal value of $\sin^{-1}\tan\big(\large\frac{-5\pi}{4}\big)$ is


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$\Rightarrow \sin^{-1}\{-\tan(\pi+\large\frac{\pi}{4})\}$
$\Rightarrow \sin^{-1}\big(-\tan\large\frac{\pi}{4}\big)$
We know that $\tan\large\frac{\pi}{4}$$=1$
Hence $\sin^{-1}\big(-1\big)=-\sin^{-1}(1)$
Hence (d) is the correct answer.
answered Oct 11, 2013 by sreemathi.v

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