Question

Докажите тоджество:

sin^2 (a+B) - sin^2 (a-B)=sin 2a sin2B

Answer 1

sin^2 (a+B) - sin^2 (a-B)=sin 2a sin2B

(sin (a+B) - sin (a-B))*(sin (a+B) + sin (a-B))=sin 2a sin2B

(sina*cosB+sinB*cosa-sina*cosB+sinB*cosa)*(sina*cosB+sinB*cosa+sina*cosB-sinB*cosa)=sin 2a sin2B

2sinB*cosa*2sina*cosB=sin 2a sin2B

sin 2a sin2B=sin 2a sin2B