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...
$\displaystyle x=\tan \theta+\sec \theta\Longrightarrow x=\frac{\sin \theta+1}{\cos \theta}$ , so:
$\displaystyle \frac{x^2-1}{x^2+1}=\frac{\frac{\sin^2\theta+2\sin \theta+1}{\cos^2\theta} -1}{\frac{\sin^2 \theta+2\sin \theta+1}{\cos^2 \theta}+1}=\frac{\sin^2\theta+2\sin \theta+1-\cos^2\theta}{\sin^2\theta+2\sin \theta+1+\cos^2\theta}$ $\displaystyle =\frac{2\sin^2\theta+2\sin \theta}{2+2\sin \theta}=\sin \theta$
Tonio