# Inverse Trigonometric Functions · Mathematics · MHT CET

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MHT CET 2023 14th May Evening Shift
If $$\sum_\limits{r=1}^{50} \tan ^{-1} \frac{1}{2 r^2}=p$$ then $$\tan p$$ is
MHT CET 2023 14th May Evening Shift
If $$\cos ^{-1} x-\cos ^{-1} \frac{y}{3}=\alpha$$, where $$-1 \leq x \leq 1, -3 \leq y \leq 3, x \leq \frac{y}{3}$$, then for all $$x, y, 9 x^2-6 x ... MHT CET 2023 14th May Evening Shift The value of$$\tan ^{-1}\left(\frac{1}{8}\right)+\tan ^{-1}\left(\frac{1}{2}\right)+\tan ^{-1}\left(\frac{1}{5}\right)$$is MHT CET 2023 14th May Evening Shift Given$$0 \leq x \leq \frac{1}{2}$$, then the value of$$\tan \left(\sin ^{-1}\left(\frac{x}{\sqrt{2}}+\frac{\sqrt{1-x^2}}{\sqrt{2}}\right)-\sin ^{-1}...
MHT CET 2023 14th May Morning Shift
If $$\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=3 \pi$$, then the value of $$x^{2025}+x^{2026}+x^{2027}$$ is
MHT CET 2023 13th May Evening Shift
The value of $$\tan \left(\sin ^{-1}\left(\frac{3}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)$$ is
MHT CET 2023 13th May Evening Shift
If $$\left(\tan ^{-1} x\right)^2+\left(\cot ^{-1} x\right)^2=\frac{5 \pi^2}{8}$$, then the value of $$x$$ is
MHT CET 2023 13th May Evening Shift
The principal value of $$\sin ^{-1}(\sin (3 \pi / 4))$$ is
MHT CET 2023 13th May Morning Shift
$$x, y, z$$ are in G.P. and $$\tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z$$ are in A.P., then
MHT CET 2023 12th May Evening Shift
The value of $$x$$, for which $$\sin \left(\cot ^{-1}(x)\right)=\cos \left(\tan ^{-1}(1+x)\right)$$, is
MHT CET 2023 12th May Evening Shift
If $$\tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x$$, then $$x$$ is
MHT CET 2023 12th May Morning Shift
If $$x=\operatorname{cosec}\left(\tan ^{-1}\left(\cos \left(\cot ^{-1}\left(\sec \left(\sin ^{-1} a\right)\right)\right)\right)\right), \mathrm{a} \in... MHT CET 2023 12th May Morning Shift The value of$$\sin \left(\cot ^{-1} x\right)$$is MHT CET 2023 11th May Evening Shift If$$\cos ^{-1} \sqrt{\mathrm{p}}+\cos ^{-1} \sqrt{1-\mathrm{p}}+\cos ^{-1} \sqrt{1-\mathrm{q}}=\frac{3 \pi}{4}$$, then$$\mathrm{q}$$is MHT CET 2023 11th May Evening Shift$$\pi+\left(\sin ^{-1} \frac{4}{5}+\sin ^{-1} \frac{5}{13}+\sin ^{-1} \frac{16}{65}\right)$$is equal to MHT CET 2023 11th May Morning Shift If$$\alpha=3 \sin ^{-1} \frac{6}{11}$$and$$\beta=3 \cos ^{-1}\left(\frac{4}{9}\right)$$, where the inverse trigonometric functions take only the pr... MHT CET 2023 11th May Morning Shift$$\text { The value of } \sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right) \text { is }$$MHT CET 2023 11th May Morning Shift The value of$$2 \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{7}$$MHT CET 2023 11th May Morning Shift$$\text { If } y=\sqrt{\frac{1-\sin ^{-1}(x)}{1+\sin ^{-1}(x)}} \text {, then } \frac{\mathrm{d} y}{\mathrm{~d} x} \text { at } x=0 \text { and } y=1 ...
MHT CET 2023 10th May Evening Shift
The domain of the function $$\mathrm{f}(x)=\sin ^{-1}\left(\frac{|x|+5}{x^2+1}\right)$$ is $$(-\infty,-a] \cup[a, \infty)$$. Then a is equal to
MHT CET 2023 10th May Evening Shift
The value of $$\tan ^{-1}(1)+\cos ^{-1}\left(-\frac{1}{2}\right)+\sin ^{-1}\left(-\frac{1}{2}\right)$$ is
MHT CET 2023 10th May Evening Shift
If $$\tan ^{-1} a+\tan ^{-1} b+\tan ^{-1} c=\pi$$, then which of the following statement is true?
MHT CET 2023 10th May Morning Shift
Considering only the principal values of an inverse function, the set $$\mathrm{A}=\left\{x \geq 0 / \tan ^{-1} x+\tan ^{-1} 6 x=\frac{\pi}{4}\right\}... MHT CET 2023 10th May Morning Shift The solution of the equation$$\tan ^{-1}(1+x)+\tan ^{-1}(1-x)=\frac{\pi}{2}$$is MHT CET 2023 9th May Evening Shift The value of$$\tan ^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right), |x|
MHT CET 2023 9th May Morning Shift
If $$\sin ^{-1} x+\cos ^{-1} y=\frac{3 \pi}{10}$$, then the value of $$\cos ^{-1} x+\sin ^{-1} y$$ is
MHT CET 2023 9th May Morning Shift
The value of $$\cot \left(\sum_\limits{n=1}^{23} \cot ^{-1}\left(1+\sum_\limits{k=1}^n 2 k\right)\right)$$ is
MHT CET 2023 9th May Morning Shift
If $$\cos ^{-1} x-\cos ^{-1} \frac{y}{3}=\alpha$$, where $$-1 \leq x \leq 1, -3 \leq y \leq 3, x \leq \frac{y}{3}$$, then for all $$x, y$$ $$9 x^2-6 x... MHT CET 2022 11th August Evening Shift If$$\tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x$$, then$$x$$has the value MHT CET 2022 11th August Evening Shift The value of$$\sin \left(2 \sin ^{-1} 0.8\right)$$is equal to MHT CET 2022 11th August Evening Shift The principal value of$$\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$$is MHT CET 2021 24th September Evening Shift The value of$$\tan ^{-1} 2+\tan ^{-1} 3$$is MHT CET 2021 24th September Morning Shift If$$y=\tan ^{-1}\left[\frac{\log \left(\frac{e}{x^2}\right)}{\log \left(e x^2\right)}\right]+\tan ^{-1}\left[\frac{3+2 \log x}{1-6 \log x}\right]$$, ... MHT CET 2021 24th September Morning Shift The value of$$\sin ^{-1}\left(\frac{-1}{2}\right)+\sin ^{-1}\left(\frac{-\sqrt{3}}{2}\right)$$is, MHT CET 2021 23rd September Evening Shift If$$\tan ^{-1}(2 x)+\tan ^{-1}(3 x)=\frac{\pi}{4}$$, where$$x>0$$, then$$x=$$MHT CET 2021 23th September Morning Shift$$\tan \left(\cos ^{-1}\left(\frac{4}{5}\right)+\tan ^{-1}\left(\frac{2}{3}\right)\right)=$$MHT CET 2021 23th September Morning Shift If$$\tan ^{-1}\left[\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right]=\alpha$$, then the value of$$\sin 2 \alpha$$is MHT CET 2021 22th September Evening Shift If$$2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x)$$, then the value of$$x$$is MHT CET 2021 22th September Morning Shift$$\tan ^{-1}\left(\tan \frac{5 \pi}{6}\right)+\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)=$$MHT CET 2021 22th September Morning Shift$$y=\tan ^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right), 0 \leq x
MHT CET 2021 21th September Evening Shift
If $$y=\tan ^{-1}\left[\frac{1}{1+x+x^2}\right]+\tan ^{-1}\left[\frac{1}{x^2+3 x+3}\right], x>0$$, then $$\frac{d y}{d x}=$$
MHT CET 2021 21th September Evening Shift
If $$\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)=\sin ^{-1} \alpha$$, then $$\alpha=$$
MHT CET 2021 21th September Morning Shift
$$\tan ^{-1}\left(\frac{x-1}{x-2}\right)+\tan ^{-1}\left(\frac{x+1}{x+2}\right)=\frac{\pi}{4}$$, then the values of $$x$$ are
MHT CET 2021 20th September Evening Shift
$$\sin ^{-1}\left[\sin \left(-600^{\circ}\right)\right]+\cot ^{-1}(-\sqrt{3})=$$
MHT CET 2021 20th September Evening Shift
$$\cos ^{-1}\left(\frac{4}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)=$$
MHT CET 2021 20th September Morning Shift
If $$4 \sin ^{-1} x+6 \cos ^{-1} x=3 \pi$$, where $$-1 \leq x \leq 1$$, then $$x=$$
MHT CET 2020 16th October Morning Shift
The value of $$\sin ^{-1}\left(-\frac{1}{2}\right)+\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$ is
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