Question

2tan 30
1+tan²30°
= sin60​

Answer 1

Step-by-step explanation:

sin60° = √3/2

(2tan30°)/(1 + tan²30°)

we know, tan30° = 1/√3

so, (2tan30°)/(1 + tan²30°) = (2 × 1/√3)/{1 + (1/√3)²}

= (2/√3)/(1 + 1/3)

= (2/√3)/(4/3)

= 2/√3 × 3/4

= 2/√3 × (√3)²/2²

= √3/2

here it is clear that sin60° = (2tan30°)/(1 + tan²30°)

hence verified