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October 8th, 2018, 03:16 AM   #1
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Verifying Trigonometric identity

Please help me figure out this problem.

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

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

Last edited by skipjack; October 8th, 2018 at 04:20 AM.
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October 8th, 2018, 04:17 AM   #2
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$\displaystyle \cos(x-y)=\cos x\cos y+\sin x\sin y$
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October 8th, 2018, 04:23 AM   #3
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cos(X - Y) = cos(X)cos(Y) + sin(X)sin(Y) is a standard identity.
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October 8th, 2018, 04:29 AM   #4
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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.

Last edited by skipjack; October 8th, 2018 at 02:38 PM. Reason: to add missing parentheses
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October 8th, 2018, 05:41 AM   #5
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Wow. Never mind. I just had a eureka moment. I understand now. I was just waaaayyy overthinking this.
Thanks everyone!!!!
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October 8th, 2018, 02:40 PM   #6
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The second identity you mentioned should be 1 + tan²(X) = sec²(X), but isn't needed.
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