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

Solution

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

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

Solution steps

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

Solving each part separately

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

4 cos^{2} (x) - 3 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

csc (x) + 2 = 0 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{7 π}{6} + 2 πn

sin (x) = cos (2 x + 10)

sin (x) + 2 sin^{2} (x) = 1

6 cos (x) = - 6 (1 + cos (x))

sin (θ) = \frac{60 sin ( 1 5 ^{\circ} )}{400}

sin^{2} (x) - 3 cos (x) - 1 = 0