First slide

Trigonometric equations

Question

If $C o s 20^{0} = k$ and $\cos x = 2 k^{2} - 1$ , then the possible values of x between 0⁰ and 360⁰ are

Moderate

A

$140^{0}$
B

$40^{0} a n d 140^{0}$
C

$40^{0} a n d 320^{0}$
D

$50^{0} a n d 130^{0}$

Solution

$\cos 20^{0} = K; \cos x = 2 K^{2} - 1$
$= 2 \cos^{2} 20^{0} - 1 = \cos 40^{0}$
on verification $x = 40^{0} & 320^{0}$ satisfies

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