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cot(theta)tan(theta) over sin(theta) + cos(theta) equals csc(theta)  sec(theta)
how do I proof this?
 6 months ago
 6 months ago
cot(theta)tan(theta) over sin(theta) + cos(theta) equals csc(theta)  sec(theta) how do I proof this?
 6 months ago
 6 months ago

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MertsjBest ResponseYou've already chosen the best response.3
Let's use x instead of theta
 6 months ago

MertsjBest ResponseYou've already chosen the best response.3
\[\frac{\cot x\tan x}{\sin x+\cos x}=\csc x\sec x\]
 6 months ago

MertsjBest ResponseYou've already chosen the best response.3
Do I have the problem stated correctly?
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
would I have to replace cot(x) with cos(x)/sin(x)
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
and tan(x) with sin(x)/cos(x)
 6 months ago

MertsjBest ResponseYou've already chosen the best response.3
\[(\frac{\frac{\cos x}{\sin x}\frac{\sin x}{\cos x}}{\sin x+\cos x})\times \frac{\sin x \cos x}{\sin x \cos x}=\frac{\cos ^2x\sin ^2x}{\sin x \cos x(\sin x+\cos x)}\]
 6 months ago

MertsjBest ResponseYou've already chosen the best response.3
Can you get it from there?
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
sadly no? can you explain how I can simplify it more please?
 6 months ago

MertsjBest ResponseYou've already chosen the best response.3
Factor the numerator and then the cosx + sinx will cancel.
 6 months ago

alejandrop95Best ResponseYou've already chosen the best response.0
I'm still lost :(
 6 months ago

MertsjBest ResponseYou've already chosen the best response.3
@alejandrop95 This is not your question
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
how would I factor it though? I'm sorry I am new to trig.
 6 months ago

MertsjBest ResponseYou've already chosen the best response.3
Can you factor this: \[a^2b^2\]
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
I don't think you can because it doesn't have the same coefficient
 6 months ago

MertsjBest ResponseYou've already chosen the best response.3
\[\cos ^2x\sin ^2x=(\cos x\sin x)(\cos x+\sin x)\]
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
oh okay that makes sense. so would it be cossin(cos+sin)
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
then that would cancel with the denominator correct?
 6 months ago

MertsjBest ResponseYou've already chosen the best response.3
Yes. sinx + cosx will cancel
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
which will leave 1/sin(x)+cos(x)
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
using the reciprocal identities this will equal csc(x)sec(x) ?
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
cos(x)sin(x)/sin(x)+cos(x0
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
this is where I would use the reciprocal identities?
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
the cos(x) cancel and the sin(x) cancels?
 6 months ago

Diana0920Best ResponseYou've already chosen the best response.0
yay!!!! the cancel and its one,which now you are left with the csc(x) and sec(x) reciprocal identities!! Thank you!! the key idea here that I need to work on was the factoring
 6 months ago
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