SOLUTION: Verify the identity Tan (alpha sign)+ cot( beta)= tan(beta)+cot(alpha)/tan(beta) cot (alpha)

Algebra ->  Trigonometry-basics -> SOLUTION: Verify the identity Tan (alpha sign)+ cot( beta)= tan(beta)+cot(alpha)/tan(beta) cot (alpha)      Log On


   

Question 1194264: Verify the identity
Tan (alpha sign)+ cot( beta)= tan(beta)+cot(alpha)/tan(beta) cot (alpha)
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

alpha = alpha
beta = beta













tan%28alpha%29+%2B+cot%28beta%29+=+tan%28alpha%29+%2B+1%2F%28tan%28beta%29%29

tan%28alpha%29+%2B+cot%28beta%29+=+tan%28alpha%29+%2B+cot%28beta%29
This confirms the identity.

Notes:
  • On the second step, I multiplied every term by tan(alpha) to get rid of the cot(alpha) in the denominator
  • tan(x)*cot(x) = 1
  • cot(x) = 1/( tan(x) )
  • Pay careful attention to the fact that the left hand side (LHS) stays the same the entire time. I only altered the right hand side (RHS) to transform it into the LHS.
  • There isn't a hard fast rule, but usually the idea is to start with the more complicated side and try to simplify it to match the other unaltered side.