Solve 2sin2x-3sin x-1 - 0-x - -0-

2sin^2x 3sin x+1≥ 0 2sin^2 x 2sin x sin x+1≥ 0 2sin x(sin x 1) 1(sin x 1)≥ 0 (2sin x 1)(sin x 1)≥ 0 .In x ∈ [0,π] Solution is #160; ...

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Sin(A+B)Sin(A-B)

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Question

Solve $2 {sin}^{2} x - 3 sin x + 1 \geq 0, x ϵ [0, π]$

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[0, π]

2 s i n^{2} x - 3 s i n x + 1 \geq 0

x

[0, π]

2 s i n^{2} x - 3 s i n x + 1 \geq 0

c o s (π + x) \sqrt{3} s i n x = s i n (3 x \frac{π}{2}), x ϵ (- \frac{4 π}{3}, \frac{π}{2}] .

I = \int \frac{cos x}{2 {sin}^{2} x + 3 sin x + 1} d x

lim x \to π / 6 \frac{2 {sin}^{2} x + sin x - 1}{2 {sin}^{2} x - 3 sin x + 1}

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