Question

If $\sec \theta +\tan \theta =p$, the find the value of $\cos \theta$.

Answer 1

$\sec \theta +\tan \theta =p$

${\sec }^2\theta -{\tan }^2\theta =1$

$(\sec \theta +\tan \theta )$$(\sec \theta -\tan \theta )=1$

Since $\sec \theta +\tan \theta =p$

So, $\sec \theta -\tan \theta =\frac{1}{p}$

On adding we get

$2\sec \theta =p+\frac{1}{p}=\frac{p^2+1}{p}$

$⟹\cos \theta =\frac{2p}{p^2+1}$