SOLUTION: Hi, I am having trouble with my homework. I hope someone helps me with this. Prove that the following equations are identities (cotY + cosY)/(secY - cosY) = (cscY + 1)/(tan^2

Algebra ->  Trigonometry-basics -> SOLUTION: Hi, I am having trouble with my homework. I hope someone helps me with this. Prove that the following equations are identities (cotY + cosY)/(secY - cosY) = (cscY + 1)/(tan^2      Log On


   

Question 602427: Hi, I am having trouble with my homework. I hope someone helps me with this.
Prove that the following equations are identities
(cotY + cosY)/(secY - cosY) = (cscY + 1)/(tan^2 Y)

Thank you for your help.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Prove that the following equations are identities
(cotY + cosY)/(secY - cosY) = (cscY + 1)/(tan^2 Y)
**
Start with left side:
(cot+cos)/(sec-cos)
=[(cos/sin)+cos]/(1/cos)-cos)
=[(cos+cos*sin)/sin]/[(1-cos^2)/cos]
=[cos(1+sin)cos]/(sin(1-cos^2)
=cos^2(1+sin)/sin*sin^2
=(cos^2/sin^2)(1+sin)/sin
=(cot^2)/sin^2
=(tan^2)(csc+1)
Verified: left side = right side