Question

cos 2 theta is equals to 2 cos squared theta minus 1 ​

Answer 1

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Answer 2

$\theta$ = 0° or, 180°

Step-by-step explanation:

We have,

$\cos^2 \theta=2\cos^2 \theta-1$

To find, the value of  $\theta$ = ?

∴ $\cos^2 \theta=2\cos^2 \theta-1$

⇒ $2\cos^2 \theta-\cos^2 \theta-1=0$

⇒ $\cos^2 \theta-1=0$

⇒ $\cos^2 \theta=1$

⇒$\cos \theta$ = ± 1

⇒ $\cos \theta$ = 1 or,  $\cos \theta$ = - 1

We know that,

$\cos 0$ = 1    and $\cos 180$ = - 1

∴ $\cos \theta$ = 1

⇒ $\cos \theta$ = $\cos 0$

⇒ $\theta$ = 0°

Also,

$\cos \theta$ =  - 1

⇒ $\cos \theta$ = $\cos 180$

⇒ $\theta$ = 180°

Thus, $\theta$ = 0° or, 180°