Question

若8sin(π/4+α)sin(π/4-α)=1,则sin^4 a+cos^4 a=

Answer 1

8sin(π/4+α)sin(π/4-α)=1

8sin(π/4+α)cos(π/4+α)=1

4sin(π/2+2α)=1

4cos(2a)=1

cos(2a)=1/4

sin^2(2a)=15/16

sin^4 a+cos^4 a

=(sin^2 a+cos^2 a)^2-2sin^2 a*cos^2 a

=1-1/2sin^2(2a)

=1-15/32

=17/32