Prove that`(frac(cos(7x-5y)+cos(7y-5x))(sin(7x-5y)+sin(7y-5x)))=cot(x+y)`

Prove the following: cos(x+y)cos(x-y)=cos^2y-sin^2x

Prove the following: (frac(sin2x+sin2y)(sin2x-sin2y))=(frac(tan(x+y))(tan(x-y)))

Prove the following: frac(sin(x+y))(sin(x-y))=frac(tanx+tany)(tanx-tany)

If 3sin(x y)+4cos(x y)=5,t h e n(dy)/(dx)= (a) -y/x (b) (3sin(x y)+4cos(x y))/(3cos(x y)-4sin(x y)) (c) (3cos(x y)+4sin(x y))/(4cos(x y)-3sin(x y)) (d) (sin^2(a+y))/(sina)

Prove the following: (frac(sinx-sin3x+sin5x-sin7x)(cosx-cos3x-cos5x+cos7x))=cot2x

Prove the following: (frac(sin5x-2sin3x+sinx)(cos5x-cosx))=tanx

If y= log(5x^2 + 7x - 2) , find dy/dx