Question 976209
term on left over (1-sinx^2)

{cos x(1-sinx) +cos x(1+sinx)}/1-sinx^2

cos x-cosx sinx + cosx+ cosx sinx=2cosx
1-sinx^2=cosx^2

(2cosx)/(cosx^2) =2/cos x

term on right:  tanx^2+ 1=secx^2.     {sinx^2/cosx^2} +1 ={sinx^2+cosx^2/cosx^2} = 1/cosx^2=secx^2.

secx^2/sec x=sec x = 1/cos x

2* (1/cosx)= 2/cosx