My Math Forum Verifying Trigonometric identity

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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(X-Y)/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 $\displaystyle \cos(x-y)=\cos x\cos y+\sin x\sin y$
 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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