Question

Докажите тождество:

$sin^{2} \beta +sin^{2} \beta * cos^{2} \beta +cos^{4} \beta =1$

Answer 1

sin^2b+sin^2b*cos^2b+cos^4b=sin^2b(1+cos^2b)+cos^4b = (1-cos^2b)(1+cos^2b)+cos^4b = 1-cos^4b+cos^4b = 1