SOLUTION: Prove that the equation is an identity: (tan^2 B + 1)/ tanB + cotB = tanB Please show and/or explain the steps if you can as well. I would really appreciate it, since I am

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Question 602444: Prove that the equation is an identity:
(tan^2 B + 1)/ tanB + cotB = tanB

Please show and/or explain the steps if you can as well. I would really appreciate it, since I am really confused with this so I hope someone will help me. Thank you!
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Prove that the equation is an identity:
(tan^2 B + 1)/ tanB + cotB = tanB
----------
tan + cot + cot = tan
Not an identity.

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
(tan^2 B + 1)/ tanB + cotB = tanB is NOT an identity but (tan^2 B + 1)/(tanB + cotB) = tanB is an identity.

Here's why...

(tan^2 B + 1)/(tanB + cotB) = tanB

(tan^2 B + 1)/(tanB + 1/tanB) = tanB

(tan^2 B + 1)/(tan^2 B/tanB + 1/tanB) = tanB

(tan^2 B + 1)/( (tan^2 B + 1)/tanB) = tanB

(tan^2 B + 1)*(tanB/(tan^2 B + 1)) = tanB

tanB = tanB

This verifies the identity.