Q.

The no. of solutions of the equation sin1x+sin12x=π3 is 

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answer is 1.

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Detailed Solution

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The given equation is sin1x+sin12x=π3

This can be written as

sin-1x=π3-sin-12x

apply sine function both sides

x=sinπ3-sin-12x =321-4x2-122x2x=321-4x24x=3-12x2

Squaring on both sides

16x2=3-12x228x2=3x=328

Take posiitve value only, if it is negative, the angle must be negative in the given equation

so the number of solutions for the given equaiton is only one

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