The Student Room Group
Reply 1
root3cos15 - sin15

Unparseable latex formula:

\huge \tex cos15 = cos(45-30)



Unparseable latex formula:

\huge \tex sin15 = sin(45-30)



Does that help?

Sin30,45 and Cos30,45 are pretty standard results.
Reply 2
In degrees:

root3*cos15 - sin15 = root3*cos(45-30) - sin(45-30)

Using standard identities:

cos(A-B) = cosAcosB + sinAsinB
sin(A-B) = sinAcosB - cosAsinB

Which gives you:

root3*[cos45cos30 + sin45sin30] - [sin45cos30 - cos45sin30]
= root3*[1/root2 * root3/2 + 1/root2 * 1/2] - [1/root2 * root3/2 - 1/root2 * 1/2]
= 3/2*root2 + root3/2*root2 - root3/2*root2 + 1/2*root2
= 2/root2
= root2

EDIT: Apologies for treading on your toes there insparato: should have scrolled down before replying...