First slide

Properties of ITF

Question

If $S i n^{- 1} x - C o s^{- 1} x = \frac{π}{6}$ then x=

Easy

A

$\frac{\sqrt{3}}{2}$
B

$\frac{1}{2}$
C

$- \frac{1}{2}$
D

$- \frac{\sqrt{3}}{2}$

Solution

$G i v e n \sin^{- 1} x - \cos^{- 1} x = \frac{π}{6} \Rightarrow \sin^{- 1} x - (\frac{π}{2} - \sin^{- 1} x) = \frac{π}{6} \Rightarrow \sin^{- 1} x = \frac{π}{3} \Rightarrow x = \sin \frac{π}{3} = \frac{\sqrt{3}}{2}$

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