cos^2(θ)-3sin(2θ)+sin^2(θ)+2sin^2(2θ)=0

Solution

cos^{2} (θ) - 3 sin (2 θ) + sin^{2} (θ) + 2 sin^{2} (2 θ) = 0

θ = \frac{π}{4} + πn, θ = \frac{π}{12} + πn, θ = \frac{5 π}{12} + πn

Solution steps

cos^{2} (θ) - 3 sin (2 θ) + sin^{2} (θ) + 2 sin^{2} (2 θ) = 0

Rewrite using trig identities

1 + 2 sin^{2} (2 θ) - 3 sin (2 θ) = 0

Solve by substitution

sin (2 θ) = 1, sin (2 θ) = \frac{1}{2}

sin (2 θ) = 1 : θ = \frac{π}{4} + πn

sin (2 θ) = \frac{1}{2} : θ = \frac{π}{12} + πn, θ = \frac{5 π}{12} + πn

Combine all the solutions

θ = \frac{π}{4} + πn, θ = \frac{π}{12} + πn, θ = \frac{5 π}{12} + πn

tan^{2} (x) cos (x) + cos^{2} (x) = 1

sinh (x) = \frac{3}{2}

a = 2 sin (3 0^{\circ} + x) - cos (x)

3 sin^{2} (x) - 6 sin (x) = - 3

tan (\frac{x}{2}) - csc (x) = 0