Question

If $6cot\Theta +2cosec\Theta =cot\Theta +5cosec\Theta$, then the value of $cos\Theta$ is

• A. $\frac{4}{5}$
• B. $\frac{3}{5}$
• C. $\frac{5}{3}$
• D. $\frac{5}{4}$

Answer 1

The correct option is B $\frac{3}{5}$

$6\cot \theta +2\csc \theta =\cot \theta +5cosec\theta$

$\Rightarrow 5\cot \theta =3cosec\theta$

$\Rightarrow \frac{\cos \theta }{\sin \theta }=\frac{3}{5}.\frac{1}{\sin \theta }$

$\Rightarrow \cos \theta =\frac{3}{5}$

Hence, the answer is $\frac{3}{5}.$