Question

已知a属于(派,3派/2),且sin^4(a)+cos^4(a)=5/9,则sin2a=?过程___

Answer 1

[sin^2(a)+cos^2(a)]^2 =sin^4(a)+cos^4(a)+2sin^2(a)cos^2(a) =5/9+1/2sin^2(2a)=1 sin^2(2a)=8/9 2a∈(2π,3π),此时正弦函数为正,所以值为(2√2)/3