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Diana0920
 2 years ago
cot(theta)tan(theta) over sin(theta) + cos(theta) equals csc(theta)  sec(theta)
how do I proof this?
Diana0920
 2 years ago
cot(theta)tan(theta) over sin(theta) + cos(theta) equals csc(theta)  sec(theta) how do I proof this?

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Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.3Let's use x instead of theta

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.3\[\frac{\cot x\tan x}{\sin x+\cos x}=\csc x\sec x\]

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.3Do I have the problem stated correctly?

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0would I have to replace cot(x) with cos(x)/sin(x)

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0and tan(x) with sin(x)/cos(x)

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

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.3Can you get it from there?

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0sadly no? can you explain how I can simplify it more please?

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.3Factor the numerator and then the cosx + sinx will cancel.

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.3@alejandrop95 This is not your question

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0how would I factor it though? I'm sorry I am new to trig.

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.3Can you factor this: \[a^2b^2\]

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0I don't think you can because it doesn't have the same coefficient

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.3\[\cos ^2x\sin ^2x=(\cos x\sin x)(\cos x+\sin x)\]

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0oh okay that makes sense. so would it be cossin(cos+sin)

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0then that would cancel with the denominator correct?

Mertsj
 2 years ago
Best ResponseYou've already chosen the best response.3Yes. sinx + cosx will cancel

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0which will leave 1/sin(x)+cos(x)

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0using the reciprocal identities this will equal csc(x)sec(x) ?

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0cos(x)sin(x)/sin(x)+cos(x0

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0this is where I would use the reciprocal identities?

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0the cos(x) cancel and the sin(x) cancels?

Diana0920
 2 years ago
Best ResponseYou've already chosen the best response.0yay!!!! 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
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