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:

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