Question

Evaluate
$(cosec\theta -\sin \theta )(\sec \theta -\cos \theta )(\tan \theta +\cot \theta )$

• A. 1
• B. 2
• C. 3
• D. 0

Answer 1

The correct option is A 1

The value of $(cosec\theta -\sin \theta )(\sec \theta -\cos \theta )(\tan \theta +\cot \theta )$
$=(\frac{1}{\sin \theta }-\sin \theta )(\frac{1}{\cos \theta }-\cos \theta )(\frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta })$
$=\left(\frac{1-{\sin }^2\theta }{\sin \theta }\right)\left(\frac{1-{\cos }^2\theta }{\cos \theta }\right)\left(\frac{{\sin }^2\theta +{\cos }^2\theta }{\cos \theta \sin \theta }\right)$
$=\left(\frac{{\cos }^2\theta }{\sin \theta }\right)\left(\frac{{\sin }^2\theta }{\cos \theta }\right)\frac{1}{\sin \theta \cos \theta }=1$