Question

If √3tanθ = 3sinθ, find the value of sin²θ - cos²θ

Answer 1

√3tanθ = 3sinθ

√3\(\frac{sinθ}{cosθ}\) = √3 x √3sinθ

\(\frac{1}{cosθ}\) = √3

cosθ = \(\frac{1}{\sqrt{3}}\) 

Now, sin²θ - cos²θ = 1 - cos²θ - cos²θ

= 1 - 2 cos²θ

= 1 - 2 x \(\Big(\frac{1}{\sqrt{3}}\Big)^2\) 

= 1 - 2 x \(\frac{1}{3}=\frac{1}{3}\)