Multiply everything by cos(x):
sin(x) + 1 = 2cos²(x)
Rewrite cos²(x) as 1 - sin²(x):
sin(x) + 1 = 2 - 2sin²(x)
Move everything to one side:
2sin²(x) + sin(x) - 1 = 0
Now it becomes a quadratic, factor it out:
[2sin(x) - 1] [sin(x) + 1] = 0
Set each factor to equal zero:
2sin(x) - 1 = 0
2sin(x) = 1
sin(x) = 1/2
x = π/6, 5π/6
sin(x) + 1 = 0
sin(x) = -1
x = 3π/2 (extraneous)
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Overall:
x = π/6, 5π/6
I hope my answer has come to your help. Thank you for posting your question here in Brainly.
