Question

If $sec\theta +tan\theta =4$, what is the value of cos$\theta$

• A. 2/3
• B. 2/5
• C. 8/15
• D. 8/17

Answer 1

The correct option is D 8/17

$⟹\frac{1+\sin \theta }{\cos \theta }=4⟹\sin \theta =4\cos \theta -1$

Squaring on both the sides,
$\therefore {\sin }^2\theta =16{\cos }^2\theta -8\cos \theta +1$
$⟹1-{\cos }^2\theta =16{\cos }^2\theta -8\cos \theta +1$
$⟹17{\cos }^2\theta -8\cos \theta =0$

$⟹\cos \theta =8/17$