Question

If `sqrt(3) tan θ` = 1, then find the value of sin²θ – cos²θ.

Answer 1

Given that,

`sqrt(3) tan θ` = 1

⇒ tan θ = `1/sqrt(3)` = tan 30°

⇒ θ = 30°

Now, sin²θ – cos²θ = sin²30° – cos²30°

= `(1/2)^2 - (sqrt(3)/2)^2`

= `1/4 - 3/4`

= `(1 - 3)/4`

= `-2/4`

= `-1/2`