We know that 1 + cos 2x = 2 (cos x)^2 (half angle
identity)
Also, we know that the tangent function
is:
tan x = sin x/cos x
We'll manage
the right side of the equality:
(tan x)(1 + cos 2x) = (sin x)*2 (cos
x)^2/(cos x)
We'll simpliy and we'll
get:
RHS = (tan x)(1 + cos 2x) = 2sin x*cos x =
LHS
We notice that we've get the expression from the left side,
since 2sin x*cos x = sin 2x
The given identity sin 2x
= (tan x)(1 + cos 2x) is verified.
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