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Question

If sinx=3sin(x+2y),ynπ, then the absolute value of tan(x+y)tany is   


Solution

Given
sinx=3sin(x+2y)sin(x+yy)=3sin(x+y+y)sin(x+y)cosycos(x+y)siny   =3[sin(x+y)cosy+cos(x+y)siny]2sin(x+y)cosy=4cos(x+y)sinytan(x+y)=2tanytan(x+y)tany=2
So, absolute value will be 2

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