Question

$(\sec A-cosecA)(1+\tan A+\cot A)=\tan A\sec A-\cot AcosecA$.

State True or False.

• A. True
• B. False

Answer 1

The correct option is A True

$(\sec A-\cos ecA)(1+\tan A+\cot A)=\tan A\sec A-\cot A\cos ecA$
$L.H.S$
$(\sec A-\cos ecA)(1+\tan A+\cot A)$
$=\sec A+\sec A\tan A+\sec A\cot A-\cos ecA-\cos ecA\tan A-\cos ecA\cot A$
$=\sec A+\sec A\tan A+\frac{1}{\cos A}\frac{\cos A}{\sin A}-\frac{1}{\sin A}-\frac{1}{\sin A}\frac{\sin A}{\cos A}-\cos ecA\cot A$
$=\frac{1}{\cos A}+\sec A\tan A+\frac{1}{\sin A}-\frac{1}{\sin A}-\frac{1}{\cos A}-\cos ecA\cot A$
$=\tan A\sec A-\cot A\cos ecA$
$=R.H.S$
$Hence\text{the given}\text{identity is true}$