First slide

Properties of ITF

Question

The value of $\sin [\frac{π}{2} - \sin^{- 1} (- \frac{\sqrt{3}}{2})] is$

Easy

A

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

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

$\frac{1}{2}$
D

$- \frac{1}{2}$

Solution

$\sin [\frac{π}{2} - \sin^{- 1} (- \frac{\sqrt{3}}{2})] = \cos (\sin^{- 1} (- \frac{\sqrt{3}}{2})) \begin{aligned} = \cos (\cos^{- 1} \sqrt{1 - \frac{3}{4}}) \\ = \cos (\cos^{- 1} (\frac{1}{2})) = \frac{1}{2} \end{aligned}$

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