Question

2tan30°/1-tan²30° is equal to
A. cos 60°
B. sin 60°
C. tan 60°
D. sin 30°

Answer 1

Answer:

2tan30°/1-tan"2 30°

=tan30°=1/root3

=then,

=(2×1/root3)/(1-(1/root3)"2

=(2/root3)/(1-1/3)

=(2/root3)/(3-1/3)

=(2/root3)/(2/3)

=2/root3×3/2

=3/root3

=root3

tan60°= root3

Therefore

option (c) is correct

Answer 2

C. tan 60°

Step-by-step explanation:

We know tan 30° = 1/ √3

2tan 30° / 1-tan² 30° = 2 * (1/ √3) / [1 - (1/ √3)²]

 = (2/√3) / (2/3)

 = 1 / √3 / 1/3

 = 3/ √3  

2tan 30° / 1-tan² 30° = √3

tan 60°= √3

Therefore 2tan 30° / 1-tan² 30° = tan 60°

Option C is the answer.