Find all the solutions to the equation (values of x). 7sin2 (x) - 14sin (x) + 2 = - 5

x = (1 + 4n) π/2, where n = any integer

Step-by-step explanation:

7sin²x - 14sinx + 2 = - 5

Add 5 to each side: 7sin²x - 14sinx + 7 = 0

Divide each side by 7: sin²x - 2sinx + 1 = 0

Factor the perfect square: (sinx - 1) (sinx - 1) = 0

Solve: sinx - 1 = 0

Add 1 to each side: sin x = 1

Take the arcsin of each side: x = π/2

However, this is only one solution.

sinx is a periodic function, and π/2 ± 2πn is also a solution.

π/2 ± 2πn = π/2 (1 ± 4n)

We can write the general solution as x = (4n + 1) π/2 where n = any integer.