Question

Докажите тождество: sin^4 a +cos^4 a + 2 sin^2 a cos ^2 a=1

Answer 1

sin^4a-cos^4a+2cos^2a=(sin^2a-cos^2a)(sin^2a+cos^2a)+2cos^2a=sin^2a-cos^2a+2cos^2a=sin^2a+cos^2a=1