Answer:
x = 3π/2
Step-by-step explanation:
The given equation can be rewritten as a quadratic in sin(x), then solved by factoring.
<h3>Rewrite</h3>
Using the identity ...
cos²x = 1 -sin²x
the equation can be rewritten as ...
sin(x) = -(1 -sin²(x)) -1 . . . . . .substitute for cos²x
<h3>Solution</h3>
The new equation can be solved by considering it a quadratic in sin(x).
0 = sin²(x) -sin(x) -2 . . . . . . subtract sin(x)
(sin(x) -2)(sin(x) +1) = 0 . . . . factor quadratic
The solutions to this are ...
sin(x) -2 = 0 ⇒ sin(x) = 2 . . . . no solutions
sin(x) +1 = 0 ⇒ sin(x) = -1 ⇒ x = 3π/2 (one solution)
