Question

Докажите тождество sin(30° -α)+sin(30°+α)=cosα

Answer 1

sin(30°-α)+sin(30°+α)=cosα

sin(pi/6 -α)+sin(pi/6+α)=cosα

(sin(pi/6)*cosα-cos(pi/6)*sinα)+(sin(pi/6)*cosα+cos(pi/6)*sinα)=cosα

sin(pi/6)*cosα+sin(pi/6)*cosα=cosα

2sin(pi/6)*cosα=cosα

2*1/2*cosα=cosα

cosα=cosα

α=(-∞;+∞)

Ответ:α=R