2 Answers

Jakub Berezanski · Answer 1 · 2021-07-21T04:58:27+0000

Answer:

x= 120°

Explanation:

cos(2x)-cos(x)=0

$\Rightarrow 2\cos^2x-\cosx-1=$ 0 [as
$\cos(2x)=2\cos^2x-1$ ]

$\Rightarrow 2\cos^2x-2\cosx +\cosx-1=0$

$\Rightarrow 2\cos x(\cos x-1) +(\cos x-1)=0$

$\Rightarrow (\cos x-1)(2\cos x +1)=0$

$\Rightarrow \cos x-1=0 \;or\; 2\cos x +1=0$

$\Rightarrow \cos x=1 \;or\; \cos x =-1/2$

$\Rightarrow x=\cos^(-1)1 \;or\; x =\cos(-1/2)$

For
$x=\cos^(-1)1$ and 0° < x <180°

There is no possible value of x.

For
$x =\cos(-1/2)$ and 0° < x <180°

The possible value of x is

x= 120°

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