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

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

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) (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.
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