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Question

If sin-1x+sin-12x=π3 then x=


A

327

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B

37

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C

0

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D

1

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Solution

The correct option is A

327


Explanation for the correct option.

Step 1: Find the relation between angles

Given that, sin-1x+sin-12x=π3.

θ=sin-1x;ϕ=sin-12xθ+ϕ=π3ϕ=π3-θ....(1)

Step 2: Simplify the equation

Taking sin both sides in equation (1) :

sinϕ=sinπ3-θ2x=sinπ3cosθ-cosπ3sinθ2x=321-x2-x25x2=3×1-x2225x2=31-x225x2-3+3x2=028x2=3x=±327

Hence, option A is correct.


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