Question

find no of soln of(sin2x+cos2x)^(1+sin4x)=2

Answer 1

looks like a log might start it off right

Answer 2

(sin2x+cos2x)^(1+sin4x)=2

(1+sin(4x)) log(sin(2x)+cos(2x)) = log(2)

hmm, no ideas come to mind afterwards

Answer 3

maybe find some identintes to get it all into the same argument ... all of the form (kx) maybe

Answer 4

any thoughts?

Answer 5

I noticed something interesting here that may help:\[(\sin(2x)+\cos(2x))^2=\sin^2(2x)+\cos^2(2x)+2\sin(2x)\cos(2x)\]\[\text{ }=1+2\sin(2x)\cos(2x)=1+\sin(4x)\]