Question

Find all solutions
7 sin2x - 14 sin x + 2 = -5

Answer 1

Have you considered adding 5 to both sides and then:

1) Factoring, if you can: \((7\sin(x) - What)(\sin(x) - What)\)

2) Quadratic formula: \(\sin(x) = \dfrac{14\pm\sqrt{Stuff}}{2\cdot 7}\)

Ringing any bells?

Answer 2

Simplify your equation,
\[7\sin^2x-14sinx+7=0\]
Replace sinx by say, t
\[7t^2-14t+7=0\]
Remove a factor of 7,\[t^2-2t+1=0\]
Solve using quadratic equation and in the end replace your t by sin(x) again
Then take inverse sine on both sides to solve for x