Question

what is cos 15 in terms of cos 30

Answer 1

#cos15˚# can be written as #cos(60˚ - 45˚)#. We use the difference formula for cosine that states #cos(A - B) = cosAcosB + sinAsinB# to expand.

#cos15˚ = cos60˚cos45˚ + sin60˚sin45˚#

We know, by the special triangles, that #cos60˚ = 1/2#, #cos45˚ = sin45˚ = 1/sqrt(2)#and #sin60˚ = sqrt(3)/2#.

#cos15˚ = (1/2)(1/sqrt(2)) +sqrt(3)/2(1/sqrt(2))##cos15˚ = 1/(2sqrt(2)) + sqrt(3)/(2sqrt(2))##cos15˚ = (1 + sqrt(3))/(2sqrt(2))#