Question #acc87

2 Answers
Nov 6, 2017

Please refer to a Proof in the Explanation.

Explanation:

(tanx+sinx)/(1+cosx),

=(sinx/cosx+sinx)/(1+cosx),

={(sinx+sinxcosx)/cosx}/(1+cosx),

={sinxcancel((1+cosx))}/{cosxcancel((1+cosx))},

=sinx/cosx,

=tanx.

Hence, the Proof.

Nov 6, 2017

See the demonstration below:

Explanation:

Start with the equation: (tan(x)+sin(x))/(1+cos(x))=tan(x)

Move 1+cos(x) on the other side of the equal sign: tan(x)+sin(x)=(1+cos(x)) cdot tan(x)

Expand (1+cos(x)) cdot tan(x)=tan(x)+tan(x) cdot cos(x)

Use the equality tan(x)=sin(x)/cos(x): tan(x)+sin(x)=tan(x)+sin(x)/cos(x) cdot cos(x)

Simplify: tan(x)+sin(x)=tan(x)+sin(x)/cancel(cos(x)) cdot cancel(cos(x))

You are left with: tan(x)+sin(x)=tan(x)+sin(x) which is true, proving that the starting equation is also true.