Sum and Difference Formulas Question?

Question

Use the formula for the cosine of the difference of two angles. Verify the following identity:

cos a(alpha) – b(beta) / sin a(alpha) sin b(beta) = cot a(alpha) cot b(beta) + 1

Answer 1

Use a for alpha and b for beta:
Use:
cos(a - b) = cosacosb + sinasinb
cos(a - b)/sinasinb = (cosacosb + sinasinb)/sinasinb
= (cosacosb)/(sinasinb) + (sinasinb)/(sinasinb)
= (cosa/sina)(cosb/cosb) + 1
= cotacotb + 1