# Verifying Trigonometric identity

#### Kraftykuts007

Cos(X-Y)/CosXCosY = 1 + TanXTanY

I feel clueless. How do you verify this identity?
Thanks!

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#### greg1313

Forum Staff
$$\displaystyle \cos(x-y)=\cos x\cos y+\sin x\sin y$$

Forum Staff

#### Kraftykuts007

That's only as far as I got. I know that certain standard identity. What I don't understand is how to verify the whole formula to = 1+TanXTanY

How do you verify the whole equation?

(Cos(X)Cos(Y)+Sin(X)Sin(Y))/ Cos(X)Cos(Y) = 1+Tan(X)Tan(Y)

Is there something I cancel out???
I know 1+Tan(x)= Sec(X)
Am I supposed to get the left side of the equation to Sec(X)???

I'm so confused on how to completely verify this.

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#### Kraftykuts007

Wow. Never mind. I just had a eureka moment. I understand now. I was just waaaayyy overthinking this.
Thanks everyone!!!!

#### skipjack

Forum Staff
The second identity you mentioned should be 1 + tanÂ²(X) = secÂ²(X), but isn't needed.