What is difference between cos^-1(x ) and 1/cosx?

Samina - the first in an inverse trig function while the latter is reciprocal of ##cos(x)##

The argument "x" for ##cos^-1(x)## will always be the ratio of adjacent over hypotenuse. For example:

##cos^-1(1/2)= 60^o##

In other words for a right triangle, ##cos(60^o)=1/2## so the inverse of this is simply ##cos^-1(1/2)= 60^o##

For the latter using the same example, ##1/cos(x)##:

##1/cos(60^o)=1/(1/2)= 2=sec(60)##

Hope that helped