# Math Help - Proving Trigonometric Identity

1. ## Proving Trigonometric Identity

Hey guys can you prove this identity for me and please tell me how you do it. Since its my first time proving identites, I have no idea what to do.

Sin theta + Sin 2 theta
________________________ = Tan theta

1 + Cos theta + Cos 2 theta

Thanks

2. Originally Posted by itsMoeyy
Hey guys can you prove this identity for me and please tell me how you do it. Since its my first time proving identites, I have no idea what to do.

Sin theta + Sin 2 theta
________________________ = Tan theta

1 + Cos theta + Cos 2 theta

Thanks
$\color{blue}sin(2\theta) = 2sin(\theta)cos(\theta)$

$Numerator= sin(\theta)+2sin(\theta)cos(\theta) = sin(\theta)(1+2cos(\theta))$
-------------------------------------------

$\color{blue}cos(2\theta) = cos^2(\theta)-sin^2(\theta)$

$\color{blue}sin^2(\theta)+cos^2(\theta)=1$

so $cos(2\theta) = 2cos^2(\theta) -1$
--------------------------------------

$Denominator ={\color{red} 1}+cos(\theta) + 2cos^2(\theta) {\color{red}-1} = cos(\theta)(1+2cos(\theta))
$

Fraction now becomes

$L.H.S=\frac{sin(\theta){\color{red}(1+2cos(\theta) )}}{cos(\theta){\color{red}(1+2cos(\theta))}}$

$=\frac{sin(\theta)}{cos(\theta)}$

$=tan(\theta)=R.H.S
$

___________________
things in blue are formulas
things in red get canceled

3. Where are the formula's from?

4. Originally Posted by itsMoeyy
Where are the formula's from?
They are standard formulae called the double angle formulae. Look for them in your class notes or textbook.

5. Ok, but how do you put the formula's into place? Like do you subtitute them into the equation. But how?

6. Originally Posted by itsMoeyy
Ok, but how do you put the formula's into place? Like do you subtitute them into the equation. But how?
You substitute one expression for the other. eg. Replace $\sin (2 \theta)$ with $2 \sin \theta \cos \theta$ etc.