Question

Find the solutions: class 11
$2cos^{2} x - 5cosx + 2 = 0$

Answer 1

Here Is Your Ans ⤵

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Ans :-

➡General Solution :-

$x = 2n\pi \: ± \: \frac{\pi}{3}$

➡Principal Solution :-

$x = \frac{\pi}{3} , \frac{ - \pi}{3}, \frac{7\pi}{3} , \frac{5\pi}{3} ............$

Given :-

➡ $2 \: cos^{2} x - 5 \: cosx + 2 = 0$

To Find :-

➡General Solution And Principal Solution Of Given Equation

Solution :-

$\implies \: 2 \: cos^{2} x - 5 \: cosx + 2 = 0 \\ \implies \: 2 \: cos^{2} x - 4 \: cosx - cosx+ 2 = 0 \\ \implies \: 2 \: cosx \: ( \: cosx \: - 2 \: ) \: - 1 \: ( \: cosx \: - 2 \: ) = 0 \\ \implies \: ( \: 2 \: cosx - 1 \: )( \: cosx - 2 \: ) = 0$

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$for \: \: \: 2 \: cosx \: - 1 = 0 \\ \implies \: cosx = \frac{1}{2} \\ \implies \: cosx = cos \frac{\pi}{3} \\ \implies \: x = 2n\pi \: ± \: \frac{\pi}{3}$

Principal Solution :-

$\implies \: x = \frac{\pi}{3} , \frac{ - \pi}{3}, \frac{7\pi}{3} , \frac{5\pi}{3} ............ \:$

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$for \: \: \: cosx - 2 = 0 \\ \implies \: cos x = 2 \: \: ( \: it \: is \: not \: possible \: )$

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Answer 2

Step-by-step explanation:

cosx=2

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