Question

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

• A. True
• B. False

Answer 1

The correct option is B False

$\frac{\cot A+\csc A-1}{\cot A-\csc A+1}$

$=\frac{\cot A+\csc A-({\csc }^{2}A-{\cot }^{2}A)}{\cot A-\csc A+1}$

$=\frac{\cot A+\csc A-(\csc A-\cot A)(\csc A+\cot A)}{\cot A-\csc A+1}$

$=\frac{(\csc A+\cot A)(1+\cot A-\csc A)}{\cot A-\csc A+1}$

$=\csc A+\cot A$

$=\frac{1}{\sin A}+\frac{\cos A}{\sin A}$

$=\frac{1+\cos A}{\sin A}$

The given statement is true.