Question

BRAINLIEST!!! 19. Solve

Answer 1

Answer:

Θ = 0, π, $\frac{7\pi }{6}$, $\frac{11\pi }{6}$

Step-by-step explanation:

Using the identity

cos2Θ = 1 - 2sin²Θ, then

sinΘ + 1 = 1 - 2sin²Θ ( subtract 1 - 2sin²Θ from both sides )

2sin²Θ + sinΘ = 0 ← factor out sinΘ from each term

sinΘ(2sinΘ + 1) = 0

Equate each factor to zero and solve for Θ

sinΘ = 0, hence

Θ = $sin^{-1}$ (0) = 0, π, 2π

2sinΘ + 1 = 0 → sinΘ = - $\frac{1}{2}$ , thus

Θ = $sin^{-1}$ ( - $\frac{1}{2}$ ) = - $\frac{\pi }{6}$

Since sinΘ < 0 then Θ is in third/ fourth quadrants, thus

Θ = π + $\frac{\pi }{6}$ = $\frac{7\pi }{6}$ or Θ = 2π - $\frac{\pi }{6}$ = $\frac{11\pi }{6}$

Solution is

Θ = 0, π, $\frac{7\pi }{6}$, $\frac{11\pi }{6}$ for 0 ≤ Θ < 2π