Question

If `sqrt(3) tan θ - 1 = 0`, find the value of sin²θ – cos²θ.

Answer 1

Given: `sqrt(3) tan θ - 1 = 0`

Step-wise calculation:

1. `sqrt(3) tan θ - 1 = 0`

⇒ `tan θ = 1/sqrt(3)` 

So `θ = 30^circ (π/6) + kπ`.

2. Use sin²θ – cos²θ = –cos²θ.

3. For θ = 30°

2θ = 60°

And cos 2θ = cos 60° = `1/2`

4. Therefore sin²θ – cos²θ = –cos²θ = `-1/2`.