Solve the equation

Question

Cos(2Θ) + 6Sin²Θ = 2

 

Interval: 0≤Θ<2π

Answer 1

Remember the double angle formula?

 

cos(2θ) = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ.

 

Since your equation has a sin²θ, let's use the last one.

 

That makes the equation 1 - 2sin²θ + 6sin²θ = 2.

 

Subtract 1 and combine terms:  4sin²θ = 1.

 

Divide by 4 and simplify:  sin²θ = ¼.

 

Thake the square root:  sinθ = ½ and -½.

 

Therefore: θ = π/6, 5π/6, 7π/6, 11π/6.

 

I hope that helps.