Question

Find all solutions to the equation.

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

Answer 1

7sin²x-14sin x+2=-5
7sin²x-14sin x+7=0

Then: sin x=t

7t²-14t+7=0

We have to solve this square equation:
t=[14⁺₋√(196-196)]/14=14/14=1

t=1 ⇒sin x=1
x=sin⁻¹ 1=π/2 + 2kπ (k=...-3,-2,-1,0,1,2,3...)

For example:
if K=0 ⇒ x=π/2
7(sin²π/2)-14sin π/2+2=7(1)²-14(1)+2=7-14+2=-5

Answer: x=π/2 + 2kπ (k is an integer)