Find the exact value of each of the following expressions co

Find the exact value of each of the following expressions. cot(75 degree)

Solution

cot ( 75) = 1 / tan 75

tan 75 = tan (45 + 30 )

tan (a + b ) = tan a + tan b / 1 - tan a tan b

= tan 45 + tan 30 / 1 - tan (45) tan (30)

= 1 + sqrt 3 / 3 / 1- sqrt 3 /3

= ( 3 + sqrt 3 ) / ( 3 - sqrt 3 )

cot 75 = ( 3 - sqrt 3 ) / ( 3 + sqrt 3 )