# Statement I: The equation (sin–1x)3 + (cos–1 x)3 – ap 3 = 0 has a solution for all 1 a 32 ³ . Statement II: For any x R Î , 1 1 sin x cos x 2 – – p + = and 2 2 1 9 0 sin x 4 16 æ ö – p p

Question:

Statement I: The equation $\left(\sin ^{-1} x\right)^{3}+\left(\cos ^{-1} x\right)^{3}-a \pi^{3}=0$ has a solution for all $\mathrm{a} \geq \frac{1}{32}$.

Statement II: For any $x \in R, \sin ^{-1} x+\cos ^{-1} x=\frac{\pi}{2}$ and $0 \leq\left(\sin ^{-1} x-\frac{\pi}{4}\right)^{2} \leq \frac{9 \pi^{2}}{16} \quad$

1. Both statements I and II are true.

2. Both statements I and II are false.

3. Statement I is true and statement II is false.

4. Statement I is false and statement II is true.

Correct Option: 1

JEE Main Previous Year 1 Question of JEE Main from Mathematics Inverse Trigonometric Functions chapter.
JEE Main Previous Year Online April 12, 2014

Solution:

### Related Questions

• If $\alpha=\cos ^{-1}\left(\frac{3}{5}\right), \beta=\tan ^{-1}\left(\frac{1}{3}\right)$, where $0<\alpha, \beta<\frac{\pi}{2}$, then $\alpha-\beta$ is equal to:

View Solution

• A value of $x$ satisfying the equation $\sin \left[\cot ^{-1}(1+x)\right]=\cos$ $\left[\tan ^{-1} x\right]$, is :

View Solution

• The principal value of $\tan ^{-1}\left(\cot \frac{43 \pi}{4}\right)$ is:

View Solution

• The number of solutions of the equation, $\sin ^{-1} x=2 \tan ^{-1} x$ (in principal values) is :

View Solution

• A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right.$ is

View Solution

• A value of $\tan ^{-1}\left(\sin \left(\cos ^{-1}\left(\sqrt{\frac{2}{3}}\right)\right)\right.$ is

View Solution

• The largest interval lying in $\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ for which the function, $f(x)=4^{-x^{2}}+\cos ^{-1}\left(\frac{x}{2}-1\right)+\log (\cos x)$, is defined, is

View Solution

• The domain of the function $f(x)=\frac{\sin ^{-1}(x-3)}{\sqrt{9-x^{2}}}$ is

View Solution

• The trigonometric equation $\sin ^{-1} x=2 \sin ^{-1} a$ has a solution for

View Solution

• $$\cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x$$ then $\sin x=$

View Solution

error: Content is protected !!