trigonometric functions

[fiery123]

cosecx - cotx = y
find cosx in terms of y.

[Logophobic]

csc x = 1 / sin x

cot x = cos x / sin x

Substitute and solve.

[fiery123]

tried that already, doesnt work.
becomes (1-cosx)/sinx = y and cannot get rid of sinx.

[Logophobic]

I would have thought that

cos x = 1 - y sin x

was the solution.

[fiery123]

but there cannot be 'x' on that side. It must be expressed in terms of y only.

[jeff17237]

cscx-cotx=y
(cscx-cotx)(cscx+cotx)=y(cscx+cotx)
csc²x-cot²x=y(cscx+cotx)
1=y(cscx+cotx)

try it from there
if not i'll finish it for ya

[krtxmrtz]

cscx-cotx=y
1/sinx - cosx/sinx = y
(1 - cosx)/sinx = y
(1 - cosx)²/sin²x = y²
(1 - 2cosx + cos²x)/(1 - cos²x) = y²
cos²x(1 + y²) - 2cosx + 1 - y² = 0

Solving for cosx:
cosx = 1 (which is the particular case x = 0)
and
cosx = (1 - y²) / (1 + y²)

[fiery123]

thank you, thats perfect. i've been stuck on this for quite a while already.