4cos^2(t)sin(t)-2cos(t)sin(t)=0

Solution

4 cos^{2} (t) sin (t) - 2 cos (t) sin (t) = 0

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

Solution steps

4 cos^{2} (t) sin (t) - 2 cos (t) sin (t) = 0

Factor

4 cos^{2} (t) sin (t) - 2 cos (t) sin (t) : 2 sin (t) cos (t) (2 cos (t) - 1)

2 sin (t) cos (t) (2 cos (t) - 1) = 0

Solving each part separately

sin (t) = 0 or cos (t) = 0 or 2 cos (t) - 1 = 0

sin (t) = 0 : t = 2 πn, t = π + 2 πn

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

2 cos (t) - 1 = 0 : t = \frac{π}{3} + 2 πn, t = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

3 (1 - sin (θ)) = 2 cos^{2} (θ)

sin (x) = \frac{5}{5}

tan (θ) = 0.11246

cos (2 θ) - sin^{2} (θ) = 1

sin (x) = \frac{3}{4}