Question

Find all solutions to the equation.

7 sin2x - 14 sin x + 2 = -5

Answer 1

you mean
\[7\sin^2x-14\sin x+7=0\]
step 1: replace \[\sin x=u\]
then you get a quadratic.
step 2: solve the quadratic and get two values for "u"
step 3: replace "u" back with "sin x" for each case, find the values for "x"

Answer 2

When i replaced it i factored it and got (u-1)(u-1).. so are you saying it should be (sin x-1)sin x-1)?

Answer 3

yes..
more precisely,
\[u=1\implies\sin x=1\implies x=\sin^{-1}(1)\]

Answer 4

find the values of "x" now

Answer 5

since the domain is provided, there are infinite values following a recursion.. write that down.