Question

What is $\frac{\sin \theta }{cosec\theta }+\frac{\cos \theta }{\sec \theta }$ equal to ?

• A. 1
• B. 1/2
• C. 1/3
• D. 2

Answer 1

Answer: (A)

1

We know that $\text{cosec}\theta =\frac{1}{\sin \theta },\sec \theta =\frac{1}{\cos \theta }$

Then, $\frac{\sin \theta }{\text{cosec}\theta }+\frac{\cos \theta }{\sec \theta }=\frac{\sin \theta }{\left(\frac{1}{\sin \theta }\right)}+\frac{\cos \theta }{\left(\frac{1}{\cos \theta }\right)}={\sin }^2\theta +{\cos }^2\theta =1$