Can you solve this : (2 Tan ½ X) / (1 + (Tan ½ X) 2 ) = (Sin X) using half angle identities?

Answer 1

let 1/2x = t

LHS = 2 tan t/(1+tan^2 t)
= 2 tan t/ sec ^2 t
= 2 tan t cos ^2 t
= 2 (tan t cos t) cos t
= 2 sint cos t
= sin 2 t
= sin x
proved

Answer 2

do you pick the sin(2x)? The question fairly does not say. Hypotenuse = 5 adjacent = 4 opposite = ??? opposite = sqrt(5^2 - 4^2) opposite = sqrt(25 - sixteen) opposite = sqrt(9) = 3 Sin(x) = 3/5 in quadrant a million. Sin(2x) = 2 sin(x) cos(x) Sin(2x) = 2 3/5 * 4/5 sin(2x) = 24/25 be conscious that the fee (24/25) is decrease than a million.

Answer 3

Let x / 2 = A
LHS =
(2 sin A /cos A) / [1 + sin ² A / cos ² A ]
= [2 sin A / cos A] / [(cos ² A + sin ² A) / cos ²A]
= 2 sin A .cos A / 1
= sin 2A
= sin x = RHS as required

Answer 4

No. I can not solve it.