Question

If $7\csc \theta -3\cot \theta =7$, then the value of 7 $\cot \theta -3\csc \theta$ is _____.

• A. $5$
• B. $3$
• C. $\frac{3}{2}$
• D. $\frac{1}{6}$

Answer 1

Answer: (B)

$3$

Given, $7\csc \theta -3\cot \theta =7$

$7\csc \theta -7=3\cot \theta$

$7(\csc \theta -1)=3\cot \theta$

Multiply $(\csc \theta +1)$ on both sides, we get

$7(\csc \theta -1)(\csc \theta +1)=3\cot \theta (\csc \theta +1)$

$7({\csc }^2\theta -1)=3\cot \theta (csc\theta +1)$

$7{\cot }^2\theta =3\cot \theta (csc\theta +1)$

$7\cot \theta =3(\csc \theta +1)$

$7\cot \theta =3\csc \theta +3$

$7\cot \theta -3\csc \theta =3$