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anonymous
 one year ago
Verify the identity.
cotx minus pi divided by two. = tan x
anonymous
 one year ago
Verify the identity. cotx minus pi divided by two. = tan x

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misty1212
 one year ago
Best ResponseYou've already chosen the best response.1if you can use the cofunction identity this is real easy

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1since cotangnent is even, you know \[\cot(x\frac{\pi}{2})=\cos(\frac{\pi}{2}x)\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1in any case , as cotangent is odd, you have \[\cot(x\frac{\pi}{2})=\cos(\frac{\pi}{2}x)\] and the cofunction identity tells gives \[\cos(\frac{\pi}{2}x)=\tan(x)\] and you are done

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea, its tan x right?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1damn i am making a lot of typos

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1let me try again in one line \[\cot(x\frac{\pi}{2})=\cot(\frac{\pi}{2}x)=\tan(x)\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1the first equal sign because cotangent is odd the second equal sign in the cofunction identity

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1is this clear? it is really only two steps, but maybe they are not obvious

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the identity is tan x or am I lost.

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1i thought that might be the case lets go slow and take them one at a time the cofunction identities say \[\cos(\frac{\pi}{2}x)=\sin(x)\\ \csc(\frac{\pi}{2}x)=\sec(x)\\ \cot(\frac{\pi}{2}x)=\tan(x)\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1since \[\cot(\frac{\pi}{2}x)=\tan(x)\] that is the same as \[\cot(\frac{\pi}{2}x)=\tan(x)\] just change the sign of both sides

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh ok, yes it is. Thnx!! :)

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1ok and how about the first part \[\cot(x\frac{\pi}{2})=\cot(\frac{\pi}{2}x)\]?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea, that's the part that kinda got me.

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1ok lets do that slow too

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1cotangent in an "odd" function, which means \[\cot(x)=\cot(x)\] in general "odd" means \[f(x)=f(x)\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1sine and tangent are also "odd" so \[\sin(x)=\sin(x)\] etc

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1now \[(x\frac{\pi}{2})=\frac{\pi}{2}x\] right ?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1that means, since cotangent is odd, that \[\cot(x\frac{\pi}{2})=\cot(\color{red}(\frac{\pi}{2}x))=\color{red}\cos(\frac{\pi}{2}x)\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1notice the minus sign comes out of the function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh yea, this makes sense....

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1it is a bit abstract, but not too hard just realizing that \(ab=(ba)\) and therefore \(\cot(ab)=\cos(ba)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh, wow it's so much clearer now. Thank you @misty1212 for your help.

misty1212
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge \color\magenta\heartsuit\]
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