Find all solutions to the equation.

Question

7 sin^2x - 14 sin x + 2 = -5

Answer 1

The equation is 7sin²x - 14sinx + 2 = - 5.

Add 5 to each side.

7sin²x - 14sinx + 2 + 5 = 0

7sin²x - 14sinx + 7 = 0

Divide each side by 7.

sin²x - 2sinx + 1 = 0

sin²x - sinx - sinx + 1 = 0

sinx (sinx - 1) - 1(sinx - 1) = 0

(sinx - 1)(sinx - 1) = 0

sinx = 1 or sinx = 1.

sinx = 1.

Take the inverse sine on both sides.

The general solution is x = 2πn + π/2 for n Є Z.