anonymous
  • anonymous
Verify the identity. cotx minus pi divided by two. = -tan x
Pre-Algebra
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\cot (x-\frac{ \pi }{ 2 })=-\tan x\]
inkyvoyd
  • inkyvoyd
the answer is eggplants=eggplants
anonymous
  • anonymous
oh come on help me out here :( i don't know how to use the confunction identities for cot.

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anonymous
  • anonymous
cofunction*
inkyvoyd
  • inkyvoyd
tan=sin/cos cot=cos/sin sin(x-pi/2)=cos(x) etc
inkyvoyd
  • inkyvoyd
I mean my advice to you is to rewrite cot as cos/sin
anonymous
  • anonymous
cos/sin=cot so cos=sin or cos = tan or cos = sec but thats only if cos(pi/2-u) but thats not the case in my problem
anonymous
  • anonymous
my problem is (x-pi/2) not (pi/2-x)
inkyvoyd
  • inkyvoyd
do you know even odd functions? sin(-x)=-sin(x) and cos(-x)=cos(x)
anonymous
  • anonymous
yes
inkyvoyd
  • inkyvoyd
hence sin(x-pi/2)=sin(-(pi/2-x))=-sin(pi/2-x) and apologies for the typo earlier
Mertsj
  • Mertsj
\[\cot (x-\frac{\pi}{2})=\frac{\cos (x-\frac{\pi}{2})}{\sin (x-\frac{\pi}{2})}=\frac{\cos x \cos \frac{\pi}{2}+\sin x \sin \frac{\pi}{2}}{\sin x \cos \frac{\pi}{2}-\cos x \sin \frac{\pi}{2}}\]
inkyvoyd
  • inkyvoyd
o no mertsj typed something latexy that's better than what I have rip
anonymous
  • anonymous
lol its no problem and true :p
inkyvoyd
  • inkyvoyd
really though you need to negate your stuff on the inside and apply even odd functions to tak eout the negative sign and rewrite cot(x-pi/2) to cot(pi/2-x) (expand cot to cos/sin to do this)
Mertsj
  • Mertsj
\[\frac{\cos x(0)+\sin x(1)}{\sin x(0)-\cos x(1)}=\frac{\sin x}{-\cos x}=-\tan x\]
Mertsj
  • Mertsj
And now you have proven the given identity once and for all.
anonymous
  • anonymous
ooooh i see i thought you had to make both of them negative thus making it tan=-tan i get it now ty!!!
UsukiDoll
  • UsukiDoll
that was an intense one.. It probably needed one of the sum or difference identity formulas. right after rewriting cotx = cosx/sinx
UsukiDoll
  • UsukiDoll
then evaluate it at pi/2 or 90 degrees ... terms cancel and viola -tanx =- tanx

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