Question

The value of $(\sin A+\cos A)(\tan A+\cot A)-\sec A-\csc Ais$

Answer 1

$(\sin A+\cos A)(\tan A+\cos A)-\sec A-cosecA$

$(\sin A+\cos A)\left(\frac{{\sin }^{2}A+{\cos }^{2}A}{\sin A.\cos A}\right)-\sec A-cosecA$

$=\left(\frac{\sin A+\cos A}{\sin A.\cos A}\right)-\sec A-cosecA$

$=\sec A+cosecA-\sec AcosecA$

$=0$

$\therefore$ The result is zero $\left(0\right)$