verify the identity:

Question

(cosx/1+sinx) + (1+sinx/cosx) = 2secx

Answer 1

sinxcosx/cos^2x-sin^2x=tanx/1-tan^2x

Answer 2

1st:
putting all over a common denominator,
= (cos^2 + (1+sin)^2)/(cos(1+sin))
= (cos^2 + 1 + 2sin + sin^2)/(cos(1+sin))
= (2 + 2sin)/(cos(1+sin))
= 2/cos
= 2sec

Answer 3

2nd:

sin2x/cos2x = tan2x
done