Question

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

Answer 1

$\text{sec}\theta +\tan \theta =k⟹\text{sec}\theta -\tan \theta =\frac{1}{k}⟹2\text{sec}\theta =k+\frac{1}{k}⟹\cos \theta =\frac{2k}{k^2+1}$