Find all solutions to the equation.

Question

7 sin ² x- 14 sin x + 2 = -5

Answer 1

7 sin²x - 14 sinx + 2 = -5

7 sin²x - 14 sinx + 7 = 0

sin²x - 2 sinx + 1 = 0

 

Let u = sin x

 

u² - 2u + 1 = 0

 

Factors to:

 

(u-1)² = 0

u = 1

sin x = 1

x = arcsin(1)

x = (pi/2) ± 2pi*n,  n = 1, 2, 3, ...