LA

Find the domain of $g(x)=\cos^{-1}(x^{2}-1)$. Hence, find the value of x for which $g(x)=\frac{\pi}{3}$. Also, write the range of $\cos^{-1}x$ other than its principal branch.

VSA

Evaluate $\sin[\tan^{-1}\tan(\frac{3\pi}{4})]$.

VSA

Express \(\tan^{-1}(\frac{\cos~x}{1-\sin~x})\) where \(\frac{-\pi}{2}\lt x\lt \frac{\pi}{2}\) in the simplest form.

MCQ_SINGLE

If \(y=\sin^{-1}x\), \(-1 \le x \le 0\), then the range of y is

VSA

Simplify \(\sin^{-1}(\frac{x}{\sqrt{1+x^{2}}}).\)

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