SOLUTION: Verify that equation is identity . sinθ+cosθ=(2sin^2θ - 1)/(sinθ-cosθ)

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Question 506868: Verify that equation is identity .
sinθ+cosθ=(2sin^2θ - 1)/(sinθ-cosθ)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sin(x)+cos(x)=(2sin^2(x) - 1)/(sin(x)-cos(x))

sin(x)+cos(x)=(2sin^2(x) - 1)/(sin(x)-cos(x))*((sin(x)+cos(x))/(sin(x)+cos(x)))

sin(x)+cos(x)=((2sin^2(x) - 1)*(sin(x)+cos(x)))/((sin(x)-cos(x))*(sin(x)+cos(x)))

sin(x)+cos(x)=((2sin^2(x) - 1)(sin(x)+cos(x)))/(sin^2(x)-cos^2(x))

sin(x)+cos(x)=(-cos(2x))(sin(x)+cos(x)))/(sin^2(x)-cos^2(x))

sin(x)+cos(x)=(-cos(2x))(sin(x)+cos(x)))/(-cos(2x))

sin(x)+cos(x)=sin(x)+cos(x)

So this verifies the identity