Number of values of x satisfying 2sin^22x = 2cos^28x + cos10x in x ∈ left[ { - frac{π

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Trigonometrical Equations

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Number of values of $x$ satisfying $2sin^22x = 2cos^28x + cos10x$ in $x \in \left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right]$ is-

A

$10$

B

$12$

C

$14$

D

$16$

Solution

$cos16x + cos10x + cos4x = 0$

$cos10x + 2 cos10x cos6x = 0$

$cos10x = 0$ or $cos6x =-\frac{1}{2}$

$x = (2n-1)\frac{\pi }{20}$ or $x = \frac{n\pi }{3} \pm \frac{\pi }{9},n \in I$

$\therefore$ Total number of values $= 10$

Standard 11

Mathematics

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