# Prove the identity `sinx+tanx= tanx(cosx+1)` I attempted this question several times but i dont seem to understand the concept please show steps taken to get the answer thanks alot !

Lix Lemjay | Certified Educator

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`sinx + tan x = tanx (cos x + 1)`

To prove, let's try to express the right side in terms of sine and tangent. To do so, distribute tan x to cos x  + 1.

`sin x + tan x = tan x * cos x + tanx *1`

`sinx + tan x = tan x * cos x + tan x`

To simplify `tan x * cos x` , note that `tanx=(sinx)/(cosx)` .

`sin x + tan x = (sinx)/(cosx)*cosx + tanx`

`sin x + tan x = sinx + tan x`

Since expressing the right side of the equation in terms of sine and tangent functions result to the same expression at the left side, this proves that the given trigonometric equation is an identity.

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