Question

HELP SIMPLIFY (sinx/1-cosx)+(1-cosx/sinx)

Answer 1

I believe you have attempted to do it. Where were you stuck? Though the answer isn't that pretty..

Answer 2

okay so i was thinking of multiplying cosx to the numerator and denominator of the (sinx/1-cosx) so then the denominator will be sin^2x and then multiply sinx to (1-cosx/sinx) so that both denominators will bbe sin^2x is that even a good first step to take?

Answer 3

sinx/(1-cosx)*(1+cosx)/(1+cosx) + (1-cosx/sinx)

=sinx(1+cosx)/sin^2 x + (1-cosx/sinx)
=(1+cosx/sinx)+(1-cosx/sinx)
=(1+cosx+1-cosx)/sinx
=2/sinx

Answer 4

why did you do this sinx(1+cosx)/sin^2 x or how'd that happen

Answer 5

oh wait nevermind i see what you did there

Answer 6

when you multiply (1-cosx) by its conjugate (1+cosx), you get (1-cos^2 x) which is just sin^2 x --> sin^2 x + cos^2 x = 1 so 1-cos^2 x=sin^2 x

Answer 7

okay well how did that turn into (1+cosx/sinx)?

Answer 8

there is a sinx in the numerator and a sin^2 x in the denominator. so 1 of them cancels out.

Answer 9

and you got 2/sinx because the +cosx and the -cosx cancel out right?

Answer 10

because that is the remaining denominator for both terms.

Answer 11

yes

Answer 12

you can simplify it even further because 1/sinx = cscx so it can also be written as 2cscx

Answer 13

oh okay thank you this was really helpful