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mousey.rr
United States103 Posts
Proove that the left hand side = right hand side: 1) (sinx-siny)/(sinx+siny) = (tan(x-y)/2)(cot(x+y)/2) 2) sin^2(x/2) = (cscx - cotx)/(2cscx) 3) tanx/2 + cotx/2 = 2cscx Can anyone at least lead a math newb in the right direction? Any help is appreciated.  | ||
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YoUr_KiLLeR
United States3420 Posts
just gotta practice and eventually youll start to more easily see what leads to what before doing them. | ||
micronesia
United States24452 Posts
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thoraxe
United States1449 Posts
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mousey.rr
United States103 Posts
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ShOoTiNg_SpElLs
Korea (South)690 Posts
Start from LHS. Using the sum to product identity (sinx +/- siny) = 2(sin(x+/-y)/2)*(cos(x-/+y)/2), this one falls apart. (+/- -/+ just refers to the order, all first ones correlate to each other, all second ones to each other) 2) sin^2(x/2) = (cscx - cotx)/(2cscx) I would start from RHS. Expand the right side, and you'll end up with (1-cosx)/2, which turns out to be sin^2(x/2). 3) tanx/2 + cotx/2 = 2cscx Is the RHS supposed to be csc2x? Also, is the angle x/2 or (tanx)/2 and (cotx)/2 ? | ||
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skyglow1
New Zealand3962 Posts
For number 2 in case you don't know why with (1-cosx)/2 is sin^2(x/2): cos(2x) = 1-2sin^2(x) (standard double angle cos formula) so cos(x) = 1-2sin^2(x/2) (having angle on both sides) so 1-cosx = 1-(1-2sin^2(x/2)) = 2sin^2(x/2) And dividing by 2 gives sin^2(x/2). | ||
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mousey.rr
United States103 Posts
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Raithed
China7078 Posts
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ShOoTiNg_SpElLs
Korea (South)690 Posts
We get from half angle identities on tan and cot, cscx-cotx and cscx+cotx and you get the RHS. To derive the half angle identities on tan and cot, we have tan(x/2) = sqrt [(1-cosx)/(1+cosx)], and if you multiply top and bottom by sqrt(1-cosx), the result follows. | ||
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BuGzlToOnl
United States5918 Posts
On December 13 2007 10:17 micronesia wrote: Amazing... I've done tons of math courses since precalc and I haven't needed any of that stuff :-p hahahahahaha | ||
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Meta
United States6225 Posts
On December 13 2007 10:17 micronesia wrote: Amazing... I've done tons of math courses since precalc and I haven't needed any of that stuff :-p Me either.. I don't think I needed to do that stuff even in precalc lol | ||
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