Question

Find θ if 0° < θ ≤ 90°.

sin θ = `(2 tan 30°)/(1 + tan^2 30°)`

Answer 1

Given:

0° < θ ≤ 90°

sin θ = `(2 tan 30°)/(1 + tan^2 30°)`

Step 1: Trigonometric values

tan⁡30° = `1/sqrt3`

`tan^2 ⁡30° = 1/3`

Step 2: Substitute values

sin θ = `(2 ⋅ 1/sqrt3)/(1+ 1/3)`

= `(2/sqrt3)/(4/3)`

Step 3: Simplify

= `2/sqrt3 ⋅ 3/4`

= `6/(4sqrt3) = 3/(2sqrt3)`

= `sqrt3/2`

Step 4: Find θ

sin θ = `sqrt3/2 → θ = 60°`

θ = 60°