Question

can a anyone explain how to do this problems? Find all solutions to the equation.

7 sin2x - 14 sin x + 2 = -5

Answer 1

set it equal to 0

Answer 2

let sinx= x
write it as quadratic equation \[\huge\rm 7x^2 -14x +2 +5 =0\]

Answer 3

7sin2x - 14sinx + 2 = -5
7sin2x - 14sinx = -7
7(sin2x - 2sinx) = -7
sin2x - 2sinx = -1
2sinxcosx - 2sinx = -1
2sinx (cosx - 1) = -1

Now solve

2sinx = -1
cosx - 1 ==1

Answer 4

Are we looking at \[\sin ^{2}x\]
or sin2x