First, note that 47-11=61-25=36, so rearrange the left hand side to get . From this, we use the sum-to-product formulas, specifically the formula
Thus we get
We use the sum-to-product formulas again, this time using , so
, as .
Working from the geometry of the pentagon, one can find the sine and cosine for angles that are multiples of 18 degrees, and thus find that:
, , and
So we get: