6cos^2(θ)sin(θ)-3cos^2(θ)=0

Solution

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

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn, θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Solution steps

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

Factor

6 cos^{2} (θ) sin (θ) - 3 cos^{2} (θ) : 3 cos^{2} (θ) (2 sin (θ) - 1)

3 cos^{2} (θ) (2 sin (θ) - 1) = 0

Solving each part separately

cos^{2} (θ) = 0 or 2 sin (θ) - 1 = 0

cos^{2} (θ) = 0 : θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

2 sin (θ) - 1 = 0 : θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn, θ = \frac{π}{6} + 2 πn, θ = \frac{5 π}{6} + 2 πn

sin^{2} (x) + 2 sin (x) + 1 = 0, 0 \leq x < 2 π

2 + 7 cos (θ) = 4 sin^{2} (θ)

x, sinh (x) = 0

sin (a) = 0.5

2 sin^{4} (x) = cos^{2} (x)