cos x/1+sin x + 1+sin x/ cos x= 2sec x

Answer 1

I am sure you meant:
cosx/(1+sinx) + (1 + sinx)/cosx = 2secx

LS = ( cosx(cosx)) + (1+sinx)^2 )/(cosx(1+sinx))
= (cos^2x + 1 + 2sinx + sin^2 x)/(cosx(1+sinx))
= (2 + 2sinx)/(cosx(1+sinx))
= 2(1+sinx)/(cosx(1+sinx))
= 2/cosx
= 2secx
= RS