(x+ 1)^a=a*x+ 1

e^x=x+ 1

a^x=x*lna+ 1

cosx= 1-x^2/2

Lncosx = ln (1-1+cosx) = ln (1-x2/2) =-x2/2 or cosx- 1.

(cosx)^2=( 1-x^2/2)^2= 1-x^2