Question

If √3 tan theta = 3 sin theta then find value of sin²theta -cos²theta

Answer 1

root 3theta is equal to 3 sin theta after solving cos theta is equal to one upon root 3 and then the value of sin square theta minus cos square theta put sin squared theta is equal to by minus cos squared theta and I put up the value of cos theta is equal to one upon root 3 then the final answer is one upon 3

Answer 2

Step-by-step explanation:

Given: √3 tan θ = 3 sinθ

⇒ √3 (sinθ/cosθ) = 3 sinθ

⇒ √3/cosθ = 3

⇒ (1/cosθ) = 3/√3

⇒ cosθ = (1/√3)

⇒ cos²θ = (1/3).

Now,

∴ sin²θ + cos²θ = 1

⇒ sin²θ + (1/3) = 1

⇒ sin²θ = 2/3

Value of sin²θ - cos²θ

= (2/3) - (1/3)

= 1/3

Hope it helps!