Question

If $tan\theta =1$, then the value of $\frac{5sin\theta +4cos\theta }{5sin\theta -4cos\theta }$ is

• A. $\frac{1}{9}$
• B. $-9$
• C. $9$
• D. $\frac{-1}{9}$

Answer 1

Answer: (C)

$9$

Given, $\tan \theta =1$

$\tan \theta =\tan 45$

$\theta ={45}^o$

Hence, $\frac{5\sin \theta +4\cos \theta }{5\sin \theta -4\cos \theta }=\frac{\frac{5}{\sqrt{2}}+\frac{4}{\sqrt{2}}}{\frac{5}{\sqrt{2}}-\frac{4}{\sqrt{2}}}$

$=\frac{\frac{9}{\sqrt{2}}}{\frac{1}{\sqrt{2}}}$

$=9$