Which of the following is / are the value (S) of the expression?

sin A(1+ tan A) + cos A (1+ cot A) ?

1. sec A + cosec A

2. 2 cosec A ( sin A + cos A )

3. tan A + cot A ;

Select the correct answer using the code given below.& ;

$\sin A (1 + \tan A) + \cos A(1 + \cot A)$

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

= $(\sin A + \cos A) (\frac{\sin A}{\cos A} + \frac{\cos A}{\sin A})$

= $(\sin A + \cos A) (\frac{\sin^2 A + \cos^2 A}{\sin A + \cos A}$

= $\sec A + cosec A$

Thus, 1 satisfies the given equation.