Question

prove the following identity 2cos(b)-2sin(a) = (cos(2a)+cos(2b))/(sin(a)+cos(b))

Answer 1

Use the identity:

\[\cos(2u)=\cos ^{2}u-\sin^{2}u\]

to write:

\[2\cos(b)-2\sin(a)=\frac{\cos ^{2}a-\sin^{2}a + \cos ^{2}b-\sin^{2}b}{\sin(a) + \cos(b)}\]

Now, pair alternate letters on RHS, factor as difference of squares. The rest is yours.

Answer 2

I have posted the complete solution on oojih.com website, see the comment section at http://www.oojih.com/show/trigonometry/twoangles/