Question

If $16\cot \theta =12$, then $\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }=$ _____

• A. $0$
• B. $\frac{1}{7}$
• C. $\frac{3}{7}$
• D. $\frac{2}{7}$

Answer 1

Answer: (B)

$\frac{1}{7}$

$\cot \theta =\frac{12}{16}=\frac{3}{4}$ and so $\tan \theta =\frac{4}{3}$ $[\because \tan \theta =\frac{1}{\cot \theta }]$

$\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }=\frac{\tan \theta -1}{\tan \theta +1}$ (Dividing both the numerator and denominator by $\cos \theta$)

Putting values, $\frac{\frac{4}{3}-1}{\frac{4}{3}+1}=\frac{\frac{1}{3}}{\frac{7}{3}}=\frac{1}{7}$

So, $\frac{1}{7}$ is correct.