SOLUTION: Hi. How do I prove this equation to be an identity? (tanY + sec^2 Y - tan^2Y)/secY = sinY + cosY Everytime I solve this I always end up with 1 - sinY cosY = sin Y + cos Y

Algebra ->  Trigonometry-basics -> SOLUTION: Hi. How do I prove this equation to be an identity? (tanY + sec^2 Y - tan^2Y)/secY = sinY + cosY Everytime I solve this I always end up with 1 - sinY cosY = sin Y + cos Y       Log On


   



Question 602443: Hi. How do I prove this equation to be an identity?
(tanY + sec^2 Y - tan^2Y)/secY = sinY + cosY

Everytime I solve this I always end up with 1 - sinY cosY = sin Y + cos Y
I really don't know what I should do here so I hope you can help me and show me how to do this. Thank you in advance!

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
(tanY + sec^2 Y - tan^2Y)/secY = sinY + cosY

(tanY + 1)/secY = sinY + cosY

tanY/secY + 1/secY = sinY + cosY

(sinY/cosy)/(1/cosY) + 1/(1/cosY) = sinY + cosY

(sinY/cosy)*(cosY/1) + cosY = sinY + cosY

(sinYcosY)/cosY + cosY = sinY + cosY

sinY + cosY = sinY + cosY

So this verifies the identity.