Question

Whether the given equation $\frac{\cot \theta -\cos \theta }{\cot \theta +\cos \theta }=\frac{\csc \theta -1}{\csc \theta +1}$ ?

• A. True
• B. False

Answer 1

The correct option is A True

Given

$\frac{\cot \theta -\cos \theta }{\cot \theta +\cos \theta }$

$\frac{\frac{\cos \theta }{\sin \theta }-\cos \theta }{\frac{\cos \theta }{\sin \theta }+\cos \theta }$

$(\cot \theta =\frac{\cos \theta }{\sin \theta })$

$\frac{\cos \theta (\frac{1}{\sin \theta }-1)}{\cos \theta (\frac{1}{\sin \theta }+1)}$

$\frac{\csc \theta -1}{\csc \theta +1}$

$(\frac{1}{\sin \theta }=\csc \theta )$