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verify the identity of trigonometry

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(1) sinx/(1-cosx)=cscx+cotx, 0<x<pi/2
(2)(cosx)^2-(sinx)^2-sin(2x)=((cos2x)^2-(sin(2x)^2)/(cos2x+sin2x)
(3)sin(pi/4-x)=sqrt(2)/2(cosx-sinx)
(4)sin(180-x+y)=sinxcosy-cosxsiny
(5)2sinxsin3x=(1-cos2x)(1+2cos2x)
(6)sinx-cos2x=(2sinx-1)(sinx+1).

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https://brainmass.com/math/trigonometry/verifying-identity-trigonometry-472667

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The solution provides detailed explanation how to verify the identity of trigonometry.

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