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Mathematics 17 Online
OpenStudy (anonymous):

verify the identity: (sin x cos y + cos x sin y) / (cos x cos y + sin x sin y) = (tan x + tan y) / (1 - tan x tan y) i have no idea where to start, because i've never had two variables in one identity before...

OpenStudy (anonymous):

You need sum and difference formulas.

OpenStudy (anonymous):

Sorry, but I think the identity is incorrect. Is the denominator supposed to be cosxcosy - sinxsiny?

OpenStudy (anonymous):

yeah oops... sorry

OpenStudy (anonymous):

the only sum and difference formulas i have are the Pythagorean ones (sin^2 + cos^2 = 1).. what else should i be using?

OpenStudy (anonymous):

The sum and difference formula in these cases involve two variables.

OpenStudy (anonymous):

They go like this: sin(x+y) = sinxcosy + cosxsiny sin(x-y) = sinxcosy - cosxsiny cos(x+y) = cosxcosy - sinxsiny cos(x-y) = cosxcosy + sinxsiny tan(x+y) = (tanx + tany)/(1-tanxtany) tan(x-y) = (tanx - tany) /(1+tanxtany)

OpenStudy (anonymous):

wow are you serious how come i don't know this... thank you!!

OpenStudy (anonymous):

Np :D There a lot of trig identities to remember.

OpenStudy (jamesj):

But actually you don't need any those here. Compare the first term in the denominator on both sides. One is cos x cos y; the other is 1. This should suggest to you to divide the numerator and denominator of the left-hand side by cos x cos y. Do that and this becomes very, very easy.

OpenStudy (anonymous):

haha yes, that's definitely true!

OpenStudy (anonymous):

OH that makes sense too!

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