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.

1,8,15,22,29,36,43,50

step-by-step explanation: