Verify the Trigonometric Identity.

Question

sin(p-q)/cos(p) cos(q) = tan(p) - tan(q)

Answer 1

All you have to do is expand the numerator and separate into fractions and the result fallls out.

sin(p-q)/(cos(p)cos(q)) =

(sin(p)cos(q) - cos(p)sin(q))/(cos(p)cos(q)) =

sin(p)cos(q) /(cos(p)cos(q)) - cos(p)sin(q))/(cos(p)cos(q)) =

sin(p)/cos(p) - sin(q)/cos(q) =

tan(p) - tan(q)