Question

tan A ÷ 1 + sec A
+
1 + sec A ÷ tan A​

Answer 1

Step-by-step explanation:

tan A/(1 + sec A)] + [(1 + sec A)/tan A]

= [(tan2A + (1 + sec A)2]/ (1 + sec A)tan A

= [(sec2A – 1) + (1 + sec A)2]/ (1 + sec A)tan A {using the identity sec2x – tan2x = 1}

= [(sec A + 1) (sec A – 1 + 1 + sec A)]/ (1 + sec A)tan A

= 2 sec A/ tan A

= (2/cos A)/ (sin A/cos A)

= 2/sin A

= 2 cosec A