Question

Find all solutions to the equation.

7 sin2x - 14 sin x + 2 = -5

If yall can help me for Pre-Calc, that would be great.
-Thanks.

Answer 1

If the equation is

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

then rewrite the equation as

`7\sin^2x-14\sin x+7=0`

Divide boths sides by 7:

`\sin^2x-2\sin x+1=0`

Since
`x^2-2x+1=(x-1)^2`, we can factorize this as

`(\sin x-1)^2=0`

Now solve for x :

`\sin x-1=0`

`\sin x=1`

`\implies\boxed{x=\frac\pi2+2n\pi}`

where n is any integer.

If you meant sin(2x) instead, I'm not sure there's a simple way to get a solution...