Question

Prove that cos theta is equal to two cos squre theta minus one hota hai

Answer 1

Step-by-step explanation:

We have,

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

2

θ=2cos

2

θ−1

To find, the value of \thetaθ = ?

∴ \cos^2 \theta=2\cos^2 \theta-1cos

2

θ=2cos

2

θ−1

⇒ 2\cos^2 \theta-\cos^2 \theta-1=02cos

2

θ−cos

2

θ−1=0

⇒ \cos^2 \theta-1=0cos

2

θ−1=0

⇒ \cos^2 \theta=1cos

2

θ=1

⇒\cos \thetacosθ = ± 1

⇒ \cos \thetacosθ = 1 or, \cos \thetacosθ = - 1

We know that,

\cos 0cos0 = 1 and \cos 180cos180 = - 1

∴ \cos \thetacosθ = 1

⇒ \cos \thetacosθ = \cos 0cos0

⇒ \thetaθ = 0°

Also,

\cos \thetacosθ = - 1

⇒ \cos \thetacosθ = \cos 180cos180

⇒ \thetaθ = 180°

Thus, \thetaθ = 0° or, 180°