已知a是锐角且cos^4a-sin^4a=3/5,求sin2a
问题描述:
已知a是锐角且cos^4a-sin^4a=3/5,求sin2a
(2)
(sin^2a+3sinacosa-cos^2a)/(2sin^2a+cos^2a)的值
答
cos^4a-sin^4a=3/5
(cos^2a-sin^2a)(cos^2a-sin^2a)=3/5
1*(cos^2a-sin^2a)=3/5
cos^2a-sin^2a=3/5
cos2a=3/5
a是锐角,∴2a∈(0,π)
∴sin2a = √{1- (sin2a)^2} = √{1- (3/5)^2} = 4/5