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SugarRainbow
 2 years ago
help with secx/sinxsinx/cosx!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SugarRainbow
 2 years ago
help with secx/sinxsinx/cosx!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1you wanna simplify it? note that sec x = 1/cos x so it becomes \(\frac{1}{sin x cos x}  \frac{sin x}{cos x} \) if you continue to put both fractions into one , you'll notice something beautiful.

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0well i got ((1/cosx)/sinx)sinx/cos x and IDK what what to do after that unless i change cosx to 1/secx then can i cancel out the two secx?

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1The sec x cannot be "cancelled". from above, \[\frac{ 1 }{ \sin x \cos x }\frac{ \sin x }{ \cos x }=\frac{ 1\sin x(\sin x) }{ \sin x \cos x}\] and \(cos^2 x+sin^2 x =1 \) :) I think this will help.

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0but if you subtract sin from 1 how did you get 1sinx(sinx)? wouldn't it just be 1sinx?

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1hmm...I didn't subtract sin x.. \[\frac{ 1 }{ a }\frac{ 1 }{ b }=\frac{ ba }{ ab }\] I think this should clear things up.

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0but you have two things in the first one cuz it's1/sinxcosx not just 1/sinx

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1yup! :) so I multiplied sin x to \( \frac {sin x}{cos x}\) to have the same denominator.

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0oh okay then you seperated it into 1sinx(sinx) because when you multiply it you get 1sin^2x

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0but now what? cuz i know it has to equal cotx but i don't see how

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1well, since from \(cos^2x+sin^2x=1\) we know that \(cos^2 x=1sin^2 x\) so it simplifies to \(\frac{cos^2}{sin x cos x}\)=cot x

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0but there's a cosx in the denominator so how does that work if cot x =cosx/sinx?

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1well, \( \frac{cos^2 x}{ sinxcosx}\)= \(\frac{cos x cosx}{sin x cos x}\) and we can cancel the cos x from the numerator and denominator.

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0oh okay!!!! weLl thanx
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