Verifying Trigonometric identity

Oct 2018
3
0
Ohio
Please help me figure out this problem.

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

I feel clueless. How do you verify this identity?
Thanks!
 
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greg1313

Forum Staff
Oct 2008
8,007
1,174
London, Ontario, Canada - The Forest City
\(\displaystyle \cos(x-y)=\cos x\cos y+\sin x\sin y\)
 
Oct 2018
3
0
Ohio
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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Oct 2018
3
0
Ohio
Wow. Never mind. I just had a eureka moment. I understand now. I was just waaaayyy overthinking this.
Thanks everyone!!!!
 

skipjack

Forum Staff
Dec 2006
21,301
2,377
The second identity you mentioned should be 1 + tan²(X) = sec²(X), but isn't needed.