SOLUTION: Hi, I have a "Trig Identity" problem that I'm to verify. I know they are equal by substituting in a value, but I don't know how to approach it. I thought using a conjugate was the

Question 230798: Hi,
I have a "Trig Identity" problem that I'm to verify. I know they are equal by substituting in a value, but I don't know how to approach it. I thought using a conjugate was the way, but it got me nowhere. Here is the problem:
(cotX * cosX)/(cotX + cosX) = (cotX - cosX)/(cotX * cosX)
Thank you,
Lynn
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
(cotX * cosX)/(cotX + cosX) = (cotX - cosX)/(cotX * cosX)
---------
Since it's all x I'll leave it out.
Cross multiply
(cot*cos)^2 = cot^2 - cos^2
(cos^2/sin^2)*cos^2 = (cos^2/sin^2) - cos^2
Divide out cos^2
cos^2/sin^2 = (1/sin^2) - 1
cos^2/sin^2 = (1 - sin^2)/sin^2
cos^2/sin^2 = cos^2/sin^2
---------------------------
PS If you sub a value and it doesn't work, you know it's not an identity.
If a value does work, that doesn't guarantee it works for all values.

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