JEE Advanced · 2013 · 02 Jun 2013 · Paper 1 · Inverse Trigonometric Functions

More JEE Advanced questions on Inverse Trigonometric Functions

1. Considering only the principal values of the inverse trigonometric functions, the value of ${\cot }^{-1}(\cot (-11))+10\sin \left(2{\cos }^{-1}\left(\frac{1}{\sqrt{2}}\right)\right)+10\sin \left(2{\tan }^{-1}(2)\right)$ is
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2. The total number of real solutions of the equation
   

   $$\theta ={\tan }^{-1}(2\tan \theta )-\frac{1}{2}{\sin }^{-1}\left(\frac{6\tan \theta }{9+{\tan }^2\theta }\right)$$

   
   is
   (Here, the inverse trigonometric functions ${\sin }^{-1}x$ and ${\tan }^{-1}x$ assume values in …
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3. Considering only the principal values of the inverse trigonometric functions, the value of
   

   $$\tan \left({\sin }^{-1}\left(\frac{3}{5}\right)-2{\cos }^{-1}\left(\frac{2}{\sqrt{5}}\right)\right)$$

   
   is
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4. For any $\mathrm{y}\in \mathbb{R}$, let ${\cot }^{-1}(\mathrm{y})\in (0,\pi )$ and ${\tan }^{-1}(\mathrm{y})\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$. Then the sum of all the solutions of the equation …
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5. Let ${\tan }^{-1}(\mathrm{x})\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$, for $\mathrm{x}\in \mathbb{R}$. Then the number of real solutions of the equation $\sqrt{1+\cos (2x)}=\sqrt{2}{\tan }^{-1}(\tan x)$ in the set …
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6. Considering only the principal values of the inverse trigonometric functions, the value of
   

   $$\frac{3}{2}{\cos }^{-1}\sqrt{\frac{2}{2+{\pi }^2}}+\frac{1}{4}{\sin }^{-1}\frac{2\sqrt{2}\pi }{2+{\pi }^2}+{\tan }^{-1}\frac{\sqrt{2}}{\pi }$$

   
   is ____.
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