Question

The value of $(\text{cosec}\theta -\sin \theta )(\sec \theta -\cos \theta )(\tan \theta +\cot \theta )$ is

• A. $0$
• B. $1$
• C. $\tan \theta$
• D. $\cot \theta$

Answer 1

Answer: (B)

$1$

The value of $(\text{cosec}\theta -\sin \theta )(\sec \theta -\cos \theta )(\tan \theta +\cot \theta )$ is

$(\frac{1}{\sin \theta }-\sin \theta )(\frac{1}{\cos \theta }-\cos \theta )(\frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta })$
$=\left(\frac{1-{\sin }^2\theta }{\sin \theta }\right)\left(\frac{1-{\cos }^2\theta }{\cos \theta }\right)\left(\frac{1}{\sin \theta .\cos \theta }\right)$
$=\frac{{\cos }^2\theta \times {\sin }^2\theta }{{\sin }^2\theta \times {\cos }^2\theta }$

$=1$