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2tan 30°/1+tan^2 30° = (A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30°

2tan 30°/1+tan^2 30° =
 
(A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30°

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Option (A) is correct.

Substitute the of tan 30° in the given equation
tan 30° = 1/√3

2tan 30°/1+tan^2 30° = 2(1/√3)/1+(1/√3)^2= (2/√3)/(1+1/3) = (2/√3)/(4/3)

= 6/4√3
= √3/2
= sin 60°
The obtained solution is equivalent to the trigonometric ratio sin 60°

Thanks

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