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\frac{\sin\left(x\right)}{\cos\left(2x+\frac{\pi}{2}\right)}\geq \frac{-\sec\left(x\right)}{2}

Solve the inequality (sin(x))/(cos(2x+pi/2))%(-1sec(x))/2

Answer

$\frac{\frac{1}{2}\cos\left(\sqrt{2}+2x\right)}{\cos\left(x\right)}+\frac{1}{\csc\left(x\right)}\geq 0$

Step-by-step explanation

Problem

$\frac{\sin\left(x\right)}{\cos\left(2x+\frac{\pi}{2}\right)}\geq \frac{-\sec\left(x\right)}{2}$
1

Simplifying the fraction

$\frac{\sin\left(x\right)}{\cos\left(\frac{\pi }{2}+2x\right)}\geq -\frac{1}{2}\sec\left(x\right)$

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Answer

$\frac{\frac{1}{2}\cos\left(\sqrt{2}+2x\right)}{\cos\left(x\right)}+\frac{1}{\csc\left(x\right)}\geq 0$
$\frac{\sin\left(x\right)}{\cos\left(2x+\frac{\pi}{2}\right)}\geq \frac{-\sec\left(x\right)}{2}$

Main topic:

Inequalities

Used formulas:

2. See formulas

Time to solve it:

~ 0.33 seconds