Inverse functions of x x

Geometry Level 3

Determine the value of x x in the following equation.

sin ⁡ − 1 ( x ) − cos ⁡ − 1 ( x ) = π 6 \sin^{-1}(x) - \cos^{-1}(x)=\dfrac{\pi}{6}

1 2 \frac{1}{2} 2 2 \frac{\sqrt{2}}{2} no answer 3 2 \frac{\sqrt{3}}{2}

Jade Mijares by Jade Mijares , 30, Philippines

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1 solution

Sabhrant Sachan
May 3, 2016

Using Formula : sin ⁡ − 1 ( x ) + cos ⁡ − 1 ( x ) = π 2 ,We get ⟹ π 2 − 2 c o s − 1 ( x ) = π 6 ⟹ 2 c o s − 1 ( x ) = 3 π 6 − π 6 ⟹ c o s − 1 ( x ) = π 6 ⟹ x = 3 2 \text {Using Formula : } \sin^{-1}(x)+\cos^{-1}(x)=\dfrac{\pi}2 \text { ,We get }\\ \implies \dfrac{\pi}{2}-2cos^{-1}(x)=\dfrac{\pi}6 \\ \implies 2cos^{-1}(x)=\dfrac{3\pi}{6}-\dfrac{\pi}6 \\ \implies cos^{-1}(x)=\dfrac{\pi}6 \\ \implies \color{#3D99F6}{\boxed{x=\dfrac{\sqrt3}2}}

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