Question

Is LHS=RHS?

$\sqrt{\frac{\csc \theta -\cot \theta }{\csc \theta +\cot \theta }}+\sqrt{\frac{\csc \theta +\cot \theta }{\csc \theta -\cot \theta }}=2\csc \theta$

Say true or false.

• A. True
• B. False
• C. Ambiguous
• D. Data insufficient

Answer 1

Answer: (A)

True

$LHS=\sqrt{\frac{\csc \theta -\cot \theta }{\csc \theta +\cot \theta }}+\sqrt{\frac{\csc \theta +\cot \theta }{\csc \theta -\cot \theta }}=\frac{\csc \theta -\cot \theta +\csc \theta +\cot \theta }{\sqrt{{\csc }^2\theta -{\cot }^2\theta }}$
$=\frac{2\csc \theta }{1}$
$=2\csc \theta =RHS$