Q JEE MAIN 2026

Let $\alpha=3 \sin ^{-1}\left(\frac{6}{11}\right)$ and $\beta=3 \cos ^{-1}\left(\frac{4}{9}\right)$, where inverse trigonometric functions take only the principal values. Given below are...

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Q JEE MAIN 2026

If $\sin \left(\tan ^{-1}(x \sqrt{2})\right)=\cot \left(\sin ^{-1} \sqrt{1-x^2}\right), x \in(0,1)$, then the value of $x$ is:

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Q JEE MAIN 2026

\text { Let } 0

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Q JEE MAIN 2026

Let $[\cdot]$ denote the greatest integer function. If the domain of the function $f(x)=\sin ^{-1}\left(\frac{x+[x]}{3}\right)$ is $[\alpha, \beta)$, then $\alpha^2+\beta^2$...

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Q

If $\frac{\pi}{4}+\sum_{p=1}^{11} \tan ^{-1}\left(\frac{2^{p-1}}{1+2^{2 p-1}}\right)=\alpha$, then $\tan \alpha$ is equal to $\_\_\_\_$ .

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Q Jee Main 2026

Let [ • ] denote the greatest integer function. If the domain of the function $f(x)=\cos ^{-1}\left(\frac{4 x+2[x]}{3}\right)$ is $...

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Q Jee Main 2024

Let $x=\frac{m}{n}\left(\mathrm{~m}, n\right.$ are co-prime natural numbers) be a solution of the equation $\cos \left(2 \sin ^{-1} x\right)=\frac{1}{9}$ and let...

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Q JEE MAIN 2024

If the domain of the function $f(x)=\log _e\left(\frac{2 x+3}{4 x^2+x-3}\right)+\cos ^{-1}\left(\frac{2 x-1}{x+2}\right)$ is $(\alpha, \beta]$, then the value of $...

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Q Jee Main 2024

If $a=\sin ^{-1}(\sin (5))$ and $b=\cos ^{-1}(\cos (5))$, then $a^2+b^2$ is equal to

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Q JEE-Main 2024

Considering only the principal values of inverse trigonometric functions, the number of positive real values of $x$ satisfying $...

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