The solution set for the inequality sin-cos3 - - sin3-cos- where -0- is

We have sinαcos^3 α gt; sin^3 αcosα ⇒sinαcosα (cos^2 α sin^2 α) gt; 0 ⇒sin4α gt;0 ⇒ 4α∈(0,π)∪(2π,3π) ∴α∈(0,π4)∪(π2,3π4) ...

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General Solution of Trigonometric Equation

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Question

The solution set for the inequality $sin α {cos}^{3} α > {sin}^{3} α cos α$ where $α \in (0, π)$ is

(0, \frac{π}{4}) \cup (\frac{π}{2}, \frac{3 π}{4})

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(0, \frac{π}{2}) \cup (\frac{π}{2}, \frac{3 π}{4})

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(\frac{π}{4}, \frac{π}{2}) \cup (\frac{π}{2}, \frac{3 π}{4})

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(0, \frac{π}{4}) \cup (\frac{3 π}{4}, π)

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sin α {cos}^{3} α > {sin}^{3} α cos α

α \in (0, π)

α = \frac{π}{3}

{log}_{sin α} (2 - {cos}^{2} x) < {log}_{sin α} (1 - sin x)

x ϵ (0, 2 π)

x \neq \frac{π}{2}

α = \frac{π}{3},

{log}_{sin α} (2 - {cos}^{2} x) < {log}_{sin α} (1 - sin x),

x ε (0.2 π)

x \neq \frac{π}{2},

x \in (- π, π)

sin 2 x + 1 \leq c o s x + 2 sin x

({cot}^{- 1} x) ({tan}^{- 1} x) + (2 - \frac{π}{2}) {cot}^{- 1} x - 3 {tan}^{- 1} x - 3 (2 - \frac{π}{2}) > 0

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