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SugarRainbow
 2 years ago
HELP SIMPLIFY (sinx/1cosx)+(1cosx/sinx)
SugarRainbow
 2 years ago
HELP SIMPLIFY (sinx/1cosx)+(1cosx/sinx)

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Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.0I believe you have attempted to do it. Where were you stuck? Though the answer isn't that pretty..

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0okay so i was thinking of multiplying cosx to the numerator and denominator of the (sinx/1cosx) so then the denominator will be sin^2x and then multiply sinx to (1cosx/sinx) so that both denominators will bbe sin^2x is that even a good first step to take?

seitys
 2 years ago
Best ResponseYou've already chosen the best response.1sinx/(1cosx)*(1+cosx)/(1+cosx) + (1cosx/sinx) =sinx(1+cosx)/sin^2 x + (1cosx/sinx) =(1+cosx/sinx)+(1cosx/sinx) =(1+cosx+1cosx)/sinx =2/sinx

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0why did you do this sinx(1+cosx)/sin^2 x or how'd that happen

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0oh wait nevermind i see what you did there

seitys
 2 years ago
Best ResponseYou've already chosen the best response.1when you multiply (1cosx) by its conjugate (1+cosx), you get (1cos^2 x) which is just sin^2 x > sin^2 x + cos^2 x = 1 so 1cos^2 x=sin^2 x

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0okay well how did that turn into (1+cosx/sinx)?

seitys
 2 years ago
Best ResponseYou've already chosen the best response.1there is a sinx in the numerator and a sin^2 x in the denominator. so 1 of them cancels out.

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0and you got 2/sinx because the +cosx and the cosx cancel out right?

seitys
 2 years ago
Best ResponseYou've already chosen the best response.1because that is the remaining denominator for both terms.

seitys
 2 years ago
Best ResponseYou've already chosen the best response.1you can simplify it even further because 1/sinx = cscx so it can also be written as 2cscx

SugarRainbow
 2 years ago
Best ResponseYou've already chosen the best response.0oh okay thank you this was really helpful
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