4sin(θ)+4=(-3)/(sin(θ)-1)

Solution

4 sin (θ) + 4 = \frac{- 3}{sin ( θ ) - 1}

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

Solution steps

4 sin (θ) + 4 = \frac{- 3}{sin ( θ ) - 1}

Solve by substitution

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

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

sin (θ) = - \frac{1}{2} : θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Combine all the solutions

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

cos (θ) = 0.707

\frac{1}{( 1 + tan ^{2} ( o ) + 1 )} + \frac{1}{( 1 + cot ^{2} ( o ) )} = 1

9 (2 sin^{2} (x) - 1) = 0

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

sin (9 x) - cos (x) = 0