Solve "cos(15)+sin(15)" Without Calculator

[RoryP]

Homework Statement

Find the values of the following, without the use of a calculator,
cos(15)+sin(15)

Homework Equations

sin(A±B)= sinAcosB±cosAsinB
cos(A±B)= cosAcosB∓sinAsinB

The Attempt at a Solution

Without the use of a calculator i had to relate back to the 2 triangles which you get the most common values for sin, cos and tan. Namely,
sin(30)= 1/2
cos(30)= √3/2
sin(45)= 1/√2
cos(45)= 1/√2
sin(60)= √3/2
cos(60)= 1/2
sin(0)= 0
cos(0)= 1
sin(90)=1
cos(90)= 0
but i have found no use for any of these, also i didnt think tan was appropriate but I am open to correction! i tried going along the lines of gettting a trig function, with the same angle, to equal 1 so i could use the addition formulae but i had no success!
any help please guys!

 

[Mark44]

The double angle formulas for cosine can be manipulated to give half-angle formulas.
cos(2a) = cos^2(a) - sin^2(a) = 1 - 2sin^2(a) = 2cos^2(a) - 1
==> cos(a) = 1 - 2sin^2(a/2) and cos(a) = 2cos^2(a/2) - 1

Take the last two equations and solve for cos(a/2) in one and sin(a/2) in the other.