t formulae

Joel · #1 $Old$ November 4th, 2009, 04:29 AM

Hi All,

Having a shocker with this one aswell.

If x = tan theta + sec theta, use the t formulae to show that (x^2 - 1) / (x^2 + 1) = sin theta

I am lost with one. Thanks

tonio · #2 $Old$ November 4th, 2009, 05:38 AM

Quote:

Originally Posted by Joel $View Post$

Hi All,

Having a shocker with this one aswell.

If x = tan theta + sec theta, use the t formulae to show that (x^2 - 1) / (x^2 + 1) = sin theta

I am lost with one. Thanks

And you think the whole world knows what the "t formulae" is? Same things can be taught very differently in different parts of the world...

$x=\tan \theta+\sec \theta\Longrightarrow x=\frac{\sin \theta+1}{\cos \theta}$ , so:

$\frac{x^2-1}{x^2+1}=\frac{\frac{\sin^2\theta+2\sin \theta+1}{\cos^2\theta} -1}{\frac{\sin^2 \theta+2\sin \theta+1}{\cos^2 \theta}+1}=\frac{\sin^2\theta+2\sin \theta+1-\cos^2\theta}{\sin^2\theta+2\sin \theta+1+\cos^2\theta}$ $=\frac{2\sin^2\theta+2\sin \theta}{2+2\sin \theta}=\sin \theta$

Tonio