Write the solution set of the equation (2 +1)(4 +5)=0 in the inte… - Vidyadip

Question

Write the solution set of the equation $(2\cos\text{x}+1)(4\cos\text{x}+5)=0$ in the interval $[0,2\pi].$

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Answer

We have,
$(2\cos\text{x}+1)(4\cos\text{x}+5)=0$
$\Rightarrow\cos\theta=\frac{-1}{2}$ or $\cos\theta=\frac{-5}{4}$
Since $\cos\theta\neq\frac{-5}{4}$ for any value of x the only solutions of the given equation in $[0,2\pi]$ are $\text{x}=\frac{2\pi}{3},\frac{4\pi}{3}$

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