Question

(sec A +cosec)(sin A+ cosA) = 2 + sec A cosecA​

Answer 1

Above is the step by step solurion

Answer 2

Answer:

$( \sec(a) + \cosec(a) )( \sin(a) + \cos(a) \\ = \frac{1}{ \cos(a) } + \frac{1}{ \sin(a) }( \sin(a) + \cos(a) ) \\ = \frac{ \sin(a) + \cos(a) }{ \cos(a) \times \sin(a) } \times ( \sin(a) + \cos(a) ) \\ = {( \sin(a) + \cos(a) ) }^{2} \times \frac{1}{ \cos(a) \times \sin(a) } \\ = { \sin(a) }^{2} + { \cos(a) }^{2} + 2 \times \sin(a) \times \cos(a) \times \frac{1}{ \sin(a) \times \cos(a) } \\ =( 1 + 2 \sin(a) \cos(a) ) \times \frac{1}{ \sin(a) \cos(a) } \\ = \frac{1}{ \sin(a) \cos(a)} + \frac{2 \sin(a) \cos(a) }{ \sin(a) \cos(a) } \\ = sec(a)cosec(a) + 2 \\ = 2 +s ec(a)cosec(a) \: proved$