cos2a=√2÷3则sin^4a+cos^4a的值

cos2a=√2÷3则sin^4a+cos^4a的值
cos2a=√2÷3则sin^4a+cos^4a的值

cos2a=√2÷3则sin^4a+cos^4a的值
cos2a=√2÷3则
sin^4a+cos^4a
=sin^4(a)+cos^4(a) +2sin^2(a) * cos^2(a) -2sin^2(a) * cos^2(a)
= [sin^2(a) + cos^2(a)]^2 - (1/2)[2sin(a)cos(a)]^2
= 1- sin^2(2a) /2
= 1- [1- cos^2(2a)] /2
= 1- [1 -(√2÷3)^2] /2
= 1- 7/18
= 11/18
验证
a =arcsin(√2÷3)/2=0.5400
sin(a)= 0.5141
cos(a)= 0.8577
cos^4(a)+sin^4(a) = 0.6111
11/18 = 0.6111
sin^2(2a) = 1- cos^2(2a)