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 Post subject: Proving the identity
PostPosted: Sat, 19 May 2012 00:14:50 UTC 
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Joined: Fri, 18 May 2012 23:48:16 UTC
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Hello all,

Prove the identity: [cot(x)/(1+tan(-x))] + [tan(x)/(1+cot(-x))] = cot(x)+tan(x)+1

Started on LHS
(cos(x)/sin(x))/(1+tan(-x)) + (sin(x)/cos(x))/(1+cot(-x))

Correct me if I'm wrong
(cos(x)/sin(x))/[1-(sin(x)/cos(x))] + (sin(x)/cos(x))/[1-(cos(x)/sin(x))]

Further assistance on next steps would be greatly appreciated, thanks.


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 Post subject: Re: Proving the identity
PostPosted: Sat, 19 May 2012 00:23:18 UTC 
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qwkevox wrote:
Hello all,

Prove the identity: [cot(x)/(1+tan(-x))] + [tan(x)/(1+cot(-x))] = cot(x)+tan(x)+1

Started on LHS
(cos(x)/sin(x))/(1+tan(-x)) + (sin(x)/cos(x))/(1+cot(-x))

Correct me if I'm wrong
(cos(x)/sin(x))/[1-(sin(x)/cos(x))] + (sin(x)/cos(x))/[1-(cos(x)/sin(x))]

Further assistance on next steps would be greatly appreciated, thanks.


No need to do that much work, set y=\tan x, then by oddness of the function, we are seeking to prove:

${1\over y-y^2}+{y\over 1-{1\over y}}={1\over y}+y+1, and that's a simple application of finding a common denominator on the LHS and reducing.

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 Post subject: Re: Proving the identity
PostPosted: Fri, 25 May 2012 05:38:53 UTC 
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Joined: Fri, 18 May 2012 23:48:16 UTC
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Thanks!


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