若sin2a=3/5,则sin^4a+cos^4a=
问题描述：
若sin2a=3/5,则sin^4a+cos^4a=
答
∵sin2a=3/5
∴sinacosa=3/10
sin^4a+cos^4a=(sin^2a+cos^2a)^2-2sin^2acos^2a
=1-2(sinacosa)^2
=1-2(3/10)^2
=41/50
答
因为sin2a=3/5=2sinacosa,sin²a+cos²a=1
所以sin^4a+cos^4a=(sin²a+cos²a)²-2sin²acos²a
=1²-sin2a/2
=1-9/50
=41/50