Question 1:
The Graph of a trigonomertic finction is as shown. Which of the following will represent graphs of its inverse?
Question 2:
If \(y=\sin^{-1}x\), \(-1 \le x \le 0\), then the range of y is
Question 3:
The principal value of \(\sin^{-1}(\sin(-\frac{10\pi}{3}))\) is:
Question 4:
The principal value of \(\cot^{-1}(-\frac{1}{\sqrt{3}})\) is:
Question 5:
\([\sec^{-1}(-\sqrt{2})-\tan^{-1}(\frac{1}{\sqrt{3}})]\) is equal to:
Question 6:
If \(\tan^{-1}(x^{2}-y^{2})=a\), where 'a' is a constant, then \(\frac{dy}{dx}\) is:
Question 7:
Domain of \(f(x)=\cos^{-1}x+\sin x\) is :
Question 8:
Simplify \(\sin^{-1}(\frac{x}{\sqrt{1+x^{2}}}).\)
Question 9:
Find domain of \(\sin^{-1}\sqrt{x-1}\).
Question 10:
Find the domain of the function \(f(x)=\cos^{-1}(x^{2}-4).\)
Question 11:
Find the domain of \(f(x)=\sin^{-1}(-x^{2})\).
Question 12:
Express \(\tan^{-1}(\frac{\cos~x}{1-\sin~x})\) where \(\frac{-\pi}{2}\lt x\lt \frac{\pi}{2}\) in the simplest form.
Question 13:
Find the value of \(\tan^{-1}(-\frac{1}{\sqrt{3}})+\cot^{-1}(\frac{1}{\sqrt{3}})+\tan^{-1}[\sin(-\frac{\pi}{2})].\)
Question 14:
Find the domain of the function \(f(x)=\sin^{-1}(x^{2}-4).\) Also, find its range.
Question 15:
Find the principal value of \(\tan^{-1}(1)+\cos^{-1}(-\frac{1}{2})+\sin^{-1}(-\frac{1}{\sqrt{2}}).\)
Question 16:
Evaluate: \(\sec^{2}(\tan^{-1}\frac{1}{2})+cosec^{2}(\cot^{-1}\frac{1}{3})\)
Question 17:
Find value of k if \(\sin^{-1}[k~\tan(2~\cos^{-1}\frac{\sqrt{3}}{2})]=\frac{\pi}{3}.\)