Question

If √3 tan θ =1, then find the value of sin² θ - cos² θ.

Answer 1

Given: √3 tan θ = 1

⇒ tan θ = 1/√3

⇒ θ = tan^-1 (1/√3) [Taking tan inverse]

⇒ θ = 30°

To find value of sin² θ – cos² θ, substitute value of θ

We get, sin² 30° - cos²30°

= (1/2)² – (√3/2)²

= 1/4 - 3/4

= -2/4 

= -1/2