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October 8th, 2018, 04:16 AM  #1 
Newbie Joined: Oct 2018 From: Ohio Posts: 3 Thanks: 0  Verifying Trigonometric identity
Please help me figure out this problem. Cos(XY)/CosXCosY = 1 + TanXTanY I feel clueless. How do you verify this identity? Thanks! Last edited by skipjack; October 8th, 2018 at 05:20 AM. 
October 8th, 2018, 05:17 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,884 Thanks: 1088 Math Focus: Elementary mathematics and beyond 
$\displaystyle \cos(xy)=\cos x\cos y+\sin x\sin y$

October 8th, 2018, 05:23 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,962 Thanks: 1847 
cos(X  Y) = cos(X)cos(Y) + sin(X)sin(Y) is a standard identity.

October 8th, 2018, 05:29 AM  #4 
Newbie Joined: Oct 2018 From: Ohio Posts: 3 Thanks: 0 
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 03:38 PM. Reason: to add missing parentheses 
October 8th, 2018, 06:41 AM  #5 
Newbie Joined: Oct 2018 From: Ohio Posts: 3 Thanks: 0 
Wow. Never mind. I just had a eureka moment. I understand now. I was just waaaayyy overthinking this. Thanks everyone!!!! 
October 8th, 2018, 03:40 PM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,962 Thanks: 1847 
The second identity you mentioned should be 1 + tan²(X) = sec²(X), but isn't needed.


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