Determine the exact value of the expression without the use

Determine the exact value of the expression without the use of a calculator.

cos(150degrees) + cos(-30degrees)

Simplify answer using integers or fractions for any numbers in the expression.

Solution

given cos(150degrees) + cos(-30degrees)

= cos(pi-pi/6) + cos30 [ since cos(-x) = cosx

= - cospi/6 + sqrt3/2

= - sqrt3/2 + sqrt3/2

=0