Prove? sin2x=2tanx/1+tan^2x

1 Answer
Mar 21, 2018

As proved below.

Explanation:

"To prove " sin 2x = (2tanx) / (1 + tan^2x)To prove sin2x=2tanx1+tan2x

Let us start from R H S and prove it equal to L H S.

R H S = (2tan x) / (1 + tan^2x)RHS=2tanx1+tan2x

=> (2 tan x) / sec^2 x, " as " 1 + tan^2x = sec^2x, "identity"2tanxsec2x, as 1+tan2x=sec2x,identity

=> (2(sin x / cancelcos x)) / (1/cancel(cos^2x)^color(red)(cosx))

=> 2 sin x cos x = sin 2x as per sin 2x = 2 sin x cos x " identity"

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=> L H S