Find the exact value of the following expression without usi

Find the exact value of the following expression without using a calculator. sec[cos^-1 (Squareroot 3/2)] =

Solution

we have cos(30⁰)=sqrt(3)/2

sec[arccos(sqrt(3)/2)]=sec[arccos(cos(30⁰))] since cos(30⁰)=sqrt(3)/2

=sec(30⁰)

=2/sqrt(3)

sec[arccos(sqrt(3)/2)]=2/sqrt(3)