Question

ASAPFind all solutions to the equation.7 sin^2 x - 14 sin x + 2 = -5

Answer 1

Answer:

{-π/2, π/2}

Step-by-step explanation:

Rewrite this as:

7sin^2 x - 14sin x + 7 = 0.  Reduce this result by dividing all terms by 7:

sin^2 x - 2sin x + 1

Temporarily replace "sin x" with y:

y^2 - 2y + 1 = 0

Solve this through factoring:  (y - 1)^2 = 0, or y - 1 = ± 0, or y = ±1

Recalling that y = sin x, we write

sin x = ±1, whose solutions are sin x = 1 and sin x = -1

The solution of sin x = 1 is π/2 and that of sin x = -1 is -π/2

and so the solution set is {-π/2, π/2}