Докажите тождество ((1+cos a)/sin a)*(1+((1-cos a)^2/sin^2 a) = 2/sin a.

Question

Докажите тождество ((1+cos a)/sin a)*(1+((1-cos a)^2/sin^2 a) = 2/sin a.

Answer 1

1+(1-cosa)/sin²a=(sin²a+1-2cosa+cos²a)/sin²a=(2-2cosa)/sin²a=2(1-cosa)/sin²a
2)(1+cosa)/sina*(2(1-cosa)/sin²a=2(1-cos²a)/sin³a=2sin²a/sin³a=2/sina
2/sina=2/sina