identity to find the exact value cos 75 degree cos 75 degree

identity to find the exact value. cos 75 degree cos 75 degree = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

cos 75^o = cos (45^o + 30^o)

we know that cos (a + b) = cosa*cosb - sina*sinb

==> cos (45^o + 30^o) = cos45^o*cos30^o - sin45^o*sin30^o

cos45^o = 1/2 ; cos30^o = 3/2 ; sin45^o = 1/2 ; sin30^o = 1/2

==> cos (45^o + 30^o) = (1/2)(3/2) - (1/2)(1/2)

==> cos 75^o = (3 -1)/(22)