Question

If $\cos \theta -4\sin \theta =1$, then $\sin \theta +4\cos \theta =$

• A. $\pm 1$
• B. $0$
• C. $\pm 2$
• D. $\pm 4$

Answer 1

The correct option is D $\pm 4$

Given, $\cos \theta -4\sin \theta =1$

Let $\sin \theta +4\cos \theta =x$
Then $(\cos \theta -4\sin \theta {)}^2+(\sin \theta +4\cos \theta )=1+x^2$
$\Rightarrow {\cos }^2\theta +16{\sin }^2\theta +{\sin }^2\theta +16{\cos }^2\theta$ $=1+x^2$
$\Rightarrow x^2=16$

$\Rightarrow x=\pm 4$

Therefore, $\sin \theta +4\cos \theta =\pm 4$