\frac{1+cos 2x}{csc x sin 2x}= cos x
[1 + cos(2x)] / [cscx sin(2x)] = cosx
[1 + (cosx)^2 - (sinx)^2] / (1/sinx)*2sinxcosx] = cosx
[1 - (sinx)^2 + (cosx)^2] / (1/sinx)*2sinxcosx] = cosx
[2(cosx)^2] / [2cosx] = cosx
cosx = cosx
