Question

(Cos x/sin x +cos y)+(cos y/sin y-cos x)=(cos x/sin x+cos y)+(cos y/sin y+cos x)

Answer 1

Answer:

Put on a common denominator.

(cosx−cosy)(cosx+cosy)+(sinx−siny)(sinx+siny)(sinx+siny)(cosx+cosy)=0

cos2x−cos2y+sin2x−sin2y(sinx+siny)(cosx+cosy)=0

Use the pythagorean identity sin2x+cos2x=1:

1−cos2y−sin2y(sinx+siny)(cosx+cosy)=0

Use the pythagorean identity mentioned above again, except this time in the form sin2x=1−cos2x.

sin2y−sin2y(sinx+siny)(cosx+cosy