JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Inverse Trigonometric Functions

More JEE Main questions on Inverse Trigonometric Functions

1. If the domain of the function $f(x)={\cos }^{-1}\left(\frac{2x-5}{11-3x}\right)+{\sin }^{-1}\left(2x^2-3x+1\right)$ is the interval $[\alpha ,\beta ]$, then $\alpha +2\beta$ is equal to :
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2. The number of solutions of ${\tan }^{-1}4\mathrm{x}+{\tan }^{-1}6\mathrm{x}=\frac{\pi }{6}$, where $-\frac{1}{2\sqrt{6}}<x<\frac{1}{2\sqrt{6}}$ is equal to
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3. If the domain of the function $\mathrm{f}(\mathrm{x})={\sin }^{-1}\left(\frac{1}{x^2-2x-2}\right)$, is $(-\infty ,\alpha ]\cup [\beta ,\gamma ]\cup [\delta ,\infty )$, then $\alpha +\beta +\gamma +\delta$ is equal to
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4. If $\mathrm{k}=\tan \left(\frac{\pi }{4}+\frac{1}{2}{\cos }^{-1}\left(\frac{2}{3}\right)\right)+\tan \left(\frac{1}{2}{\sin }^{-1}\left(\frac{2}{3}\right)\right)$ then the number of solutions of the equation …
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5. Considering the principal values of inverse trigonometric functions, the value of the expression $\tan \left(2{\sin }^{-1}\left(\frac{2}{\sqrt{13}}\right)-2{\cos }^{-1}\left(\frac{3}{\sqrt{10}}\right)\right)$ is equal to :
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6. Let [ • ] denote the greatest integer function. If the domain of the function $f(x)={\cos }^{-1}\left(\frac{4x+2[x]}{3}\right)$ is $[\alpha ,\beta ]$, then $12(\alpha +\beta )$ is equal to :
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