Question

demuestre: 2(1+cos x) = 1- cos 2x / 1-cos x

Answer 1

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

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

2(1 + cos x) = 1 - (cos x*cos x - sen x*senx)/ 1 - cos x

2(1 + cos x)(1 - cos x) = 1 - cos² x + sen²x

2(1 - cos² x) = sen² x + sen² x

2(sen² x) = 2 sen² x

2 sen² x = 2 sen² x