1. ## Trig Identity Proof

Hi,

I've been playing around with this thing for hours trying to get it to work and have made no progress ;\. anyone know how to do this?

Prove that for all angles θ,

tan(θ)^2/sin(θ)^2=1+tan(θ)^2

any help would be much appreciated,

thanks,

Coukapecker

2. ## Re: Trig Identity Proof

Write (I use $\displaystyle x$ in stead of $\displaystyle \theta$ for a moment):
$\displaystyle \tan^2(x)=\frac{\sin^2(x)}{\cos^2(x)}$
And also write:
$\displaystyle 1+\tan^2(x)=1+\frac{\sin^2(x)}{\cos^2(x)}$ $\displaystyle =\frac{\cos^2(x)+\sin^2(x)}{\cos^2(x)}=$$\displaystyle \frac{1}{\cos^2(x)} Try to continue with this. 3. ## Re: Trig Identity Proof That's actually where I got to without assistance, but I can't figure out what to do after \displaystyle tan^2(x)/sin^2(x)=sec^2(x) 4. ## Re: Trig Identity Proof You have everything to prove the identity: LHS: \displaystyle \frac{\frac{\sin^2(x)}{\cos^2(x)}}{\sin^2(x)}=$$\displaystyle \frac{\sin^2(x)}{\cos^2(x)}\cdot \frac{1}{\sin^2(x)}=\frac{1}{\cos^2(x)}$

RHS:
$\displaystyle 1+\tan^2(x)=\frac{1}{\cos^2(x)}$

So LHS=RHS

5. ## Re: Trig Identity Proof

Man,

I've bee staring at $\displaystyle (sin(x))^2/(cos(x))^2/(sin(x))^2)$ for like hours. Somehow managed to convince myself that you couldn't work with it.

Thanks for that :P.

6. ## Re: Trig Identity Proof

You're welcome! Also in trigonometry you still have to know the important algebraic rules .