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