Question

If √3 tan theta = 3sin theta then find the value of sin^2 theta - cos^2 theta

Answer 1

here is your answer friends

Answer 2

The value of sin² θ - cos² θ = 1/3

Given:

√3 tan θ = 3 sin θ

To find:

The value of sin² θ  - cos² θ

Solution:

Given √3 tan θ = 3 sin θ

as we know tan θ = (sin θ/cos θ)

⇒ √3 (sin θ/cos θ) = 3 sin θ  

⇒  √3 (1 /cos θ) = 3

⇒  cos θ = √3 /3  

⇒  cos θ = √3 /(√3√3)      [ ∵ √3(√3) = 3 ]  

⇒  cos θ = 1 /√3    

As we know sin² θ = 1 - cos² θ

⇒ sin² θ = 1 - (1/√3)²  = 1-1/3 = 2/3

⇒ sin² θ  - cos² θ = (2/3) - 1/3 = 1/3

The value of sin² θ - cos² θ = 1/3

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