Trig Proof

Question

Prove: tanA + cotB= cos(A-B) / cosAsinB

Answer 1

Lets work on the right side of the identity.  It should match the left side after simplifying.

 

cos(A - B) / cosAsinB

 

 

Notice that the numerator is a subtraction angle identity for cosine.

 

(cosAcosB + sinAsinB) / (cosAsinB)

 

 

Now we just divide each term in the numerator by the denominator.

 

cotB + tanA