find x: (2sinxcosx)2 + 4sin2x -1 = 0

Question

find x: (2sinxcosx)² + 4sin2x -1 = 0

Answer 1

There is a formula for sin2x=2sinxcosx

 

Substitute into original equation to obtain sin^2(2x)+4sin2x-1=0

 

Using the quadratic formula:

 

sin2x=(-4+/-sqrt(16+4))/2=-2+/-sqrt5

 

We must take the positive root since -1<=sinx<=1 for all x

 

So x=( invsin(sqrt5-2))/2=circa.119 radians