How to solve: y = (cos2x) / (1+sin2x)

Question

Good morning, can anyone please help me solve this problem? Thank you in advance. Have a nice day.

Answer 1

Rewrite the equation as 

 

y² (1+ sin2x)² = cos²2x      Then replace cos²2x with 1 - sin²2x    The result is an equation quadratic in sin2x

 

The quadratic formula can then be used to get two values for sin2x  One is  sin2x = (1- y² )/(! + y²)

the other is sin2x  = -1

The second one must be rejected as spurious because it leads to diving by zero in the original equation.  Thus

 

sin2x = (1 - y²) /( 1 + y²)

 

 x =  0.5 sin^-1 ((1-y²)/(! + y²))