72(-3cos^2(x)sin^2(x)+cos^4(x))=0

Solution

72 (- 3 cos^{2} (x) sin^{2} (x) + cos^{4} (x)) = 0

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

Solution steps

72 (- 3 cos^{2} (x) sin^{2} (x) + cos^{4} (x)) = 0

Factor

72 (- 3 cos^{2} (x) sin^{2} (x) + cos^{4} (x)) : 72 cos^{2} (x) (cos (x) + 3 sin (x)) (cos (x) - 3 sin (x))

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

Solving each part separately

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

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

cos (x) + 3 sin (x) = 0 : x = \frac{5 π}{6} + πn

cos (x) - 3 sin (x) = 0 : x = \frac{π}{6} + πn

Combine all the solutions

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

sin (\frac{x}{5}) = \frac{2}{2}

x, sin (x) = 0.6

4 cos (2 t) = 4 sin^{2} (t) + 1

tan^{2} (θ) + 2 tan (θ) = - 1

cos (a) = \frac{2}{3}