How do you use the angle difference identity to find the exact value of #cos15#?

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Answer 1 · 2016-08-30T04:30:37

#cos15˚ = (1 + sqrt(3))/(2sqrt(2))#

We can write that #cos15˚ = cos(60˚ - 45˚)#.

Using the difference identity #cos(A - B) = cosAcosB + sinAsinB#:

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

#=>1/2(1/sqrt(2)) + (sqrt(3))/2(1/sqrt(2))#

#=>1/(2sqrt(2)) + sqrt(3)/(2sqrt(2))#

#=>(1 + sqrt(3))/(2sqrt(2))#

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

Hopefully this helps!