Question

已知cos2a=3/5,求sin^4*a+cos^4*a=?

Answer 1

cos2a=3/5

(sin2a)^2= (1-(cos2a)^2 = 16/25

cos^2a - sin^2a = 3/5

(cos^2a - sin^2a )^2 = 9/25

(cos^2a - sin^2a )^2 = 9/25

sin^4*a+cos^4*a-2(sinacosa)^2 = 9/25

sin^4*a+cos^4*a-1/2(sin2a)^2 = 9/25

sin^4*a+cos^4*a = 9/25+1/2(sin2a)^2=9/25+1/2*16/25=17/25