Math, asked by Meghanasambaru, 3 days ago

if √3.tan=3.sin theta prove sin^2theta-cos^2=1/3​

Answers

Answered by amansharma264
3

EXPLANATION.

⇒ √3tanθ = 3sinθ.

As we know that,

We can write equation as,

⇒ tanθ = √3sinθ.

⇒ (sinθ)/(cosθ) = √3sinθ.

⇒ 1/(cosθ) = √3.

⇒ √3cosθ = 1.

⇒ cosθ = 1/(√3).

⇒ cos²θ = (1/√3)².

⇒ cos²θ = 1/3.

As we know that,

Formula of :

⇒ sin²θ + cos²θ = 1.

Using this formula in the equation, we get.

⇒ sin²θ = 1 - cos²θ.

⇒ sin²θ = 1 - (1/3).

⇒ sin²θ = (3 - 1)/(3).

⇒ sin²θ = 2/3.

To prove : sin²θ - cos²θ = 1/3.

⇒ 2/3 - 1/3 = 1/3.

Hence Proved.

Answered by kvalli8519
0

Refer the given attachment

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