Question

State whether the following statement is true or false.

$\frac{\cot A-\cos A}{\cot A+\cos A}=\frac{\text{cosec}A-1}{\text{cosec}A+1}$

• A. True
• B. False

Answer 1

The correct option is A True

$LHS=\frac{(cotA-cosA)}{(cotA+cosA)}$

$=\frac{(\frac{cosA}{sinA}-cosA)}{(\frac{cosA}{sinA}+cosA)}$

$=\frac{cosA(\frac{1}{sinA}-1)}{cosA(1/sinA+1)}$

$=\frac{(\frac{1}{sinA}-1)}{(\frac{1}{sinA}+1)}$

$=\frac{(cosecA-1)}{(cosecA+1)}$..............[ since $1/sinA=cosecA$]

$=RHS$