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Question

The principal value of $$\displaystyle \:\sin ^{-1}\left \{ \cos \left ( \sin ^{-1}\dfrac{\sqrt{3}}{2} \right ) \right \}$$ is


A
π6
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B
π3
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C
π3
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D
none of these
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Solution

The correct option is A $$\displaystyle \: \frac{\pi }{6}$$
The principle value of $$\sin^{-1}(\cos(\sin^{-1}(\dfrac{\sqrt{3}}{2})))$$

$$=\dfrac{\pi}{2}-\cos^{-1}(\cos(\sin^{-1}(\dfrac{\sqrt{3}}{2})))$$

$$=\dfrac{\pi}{2}-\sin^{-1}(\dfrac{\sqrt{3}}{2})$$

$$=\cos^{-1}(\dfrac{\sqrt{3}}{2})$$

$$=\dfrac{\pi}{6}$$

Mathematics

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