SOLUTION: Verify that each equation is an identity. {{{cos(alpha-beta)/cos(alpha)sin(beta)}}} = tan(alpha)+cot(beta)

Algebra ->  Trigonometry-basics -> SOLUTION: Verify that each equation is an identity. {{{cos(alpha-beta)/cos(alpha)sin(beta)}}} = tan(alpha)+cot(beta)      Log On


   

Question 675437: Verify that each equation is an identity.
cos%28alpha-beta%29%2Fcos%28alpha%29sin%28beta%29 = tan(alpha)+cot(beta)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
cos%28alpha-beta%29%2Fcos%28alpha%29sin%28beta%29+=+tan%28alpha%29%2Bcot%28beta%29
Since the arguments on the right side are just alpha and beta, I'm going to use the cos(A-B) formula on the numerator of the left side so that all the arguments are alpha or beta:


Since the right side has two terms I'm going to split the fraction on the left into two terms:


Each of the new fractions will reduce:


The first fraction is cot and the second is tan:
cot%28beta%29+%2B+tan%28alpha%29+=+tan%28alpha%29%2Bcot%28beta%29

Since addition is commutative we can change the order:
tan%28alpha%29+%2B+cot%28beta%29+=+tan%28alpha%29%2Bcot%28beta%29