Evaluate the expression without using a calculator Solution

Evaluate the expression without using a calculator

( sin pi/3 cos pi/4 - sin pi/4 cos pi/3 )^2

sin pi/3 = sqrt 3/2 , cos pi/3 = 1/2 , sin pi/4 = sqrt 2 /2 , cos pi/4 = sqrt 2/2

plugging the values we get

( sqrt 3/2 * sqrt 2/2 - sqrt 2/2 * 1/2 ) ^2

= ( sqrt 6 / 4 - sqrt 2 / 4 )^2

= ( 8 - 2 sqrt 12 ) / 16

= ( ( 4 - sqrt 12 ) / 8

= ( 2 - sqrt 3 ) / 4