$\sec\theta + \tan\theta=4$ find $\cos\theta$ given: $\theta\neq90$ I tried the following :
\begin{align}\sec\theta + \tan\theta&=4\\
\frac1{\cos\theta} + \frac{\sin\theta}{\cos\theta}&=4\\
\frac{1+\sin\theta}{\cos\theta}&=4\\
\frac{1+\sin\theta}4&=\cos\theta\end{align}
now don't know how to evaluate further ?

Hint: since $1+\cos\theta >0$ and $\frac{1+\cos\theta}{\sin\theta} =4$,
$\sin\theta >0$ so $\sin\theta = \sqrt{1-\cos^2\theta}$. This leads to a quadratic equation on $\cos\theta$.
