please help... college trig final.. cosx+1 / cot x = sinx+tanx?

Question

this question is straight from the book... i cannot figure out how to prove that one side equals another! i am confused on this question... *** Again*** i did not misprint the question, that is how the book had it

Answer 1

you left the parentheses off. the problem is
(cos(x) + 1) / cot(x) = sin(x) + tan(x)

Start on one side and show the other side. If starting on the left:

(cos(x) + 1) / cot(x) =
tan(x) * (cos(x) + 1) =
tan(x) * (cos(x) + tan(x) =
sin(x)/cos(x) * cos(x) + tan(x) =
sin(x) + tan(x)

Answer 2

I'm going to assume you mean (cosx + 1) on the left.

(cosx + 1)/cotx
= (cosx + 1)/(cosx/sinx)
= (cosx + 1) * (sinx/cosx)
= sinx(cosx + 1)/cosx
= (sinxcosx + sinx)/cosx
= sinxcosx / cosx + sinx / cosx
= sinx + tanx

If it's really cosx + 1/cotx, they're not equal.

But yeah, if it's not supposed to be an identity (which you said it was in the other problem) then northstar is right. The solutions are all values of x where sinx = cosx, which is pi/4 + k*pi, where k is any integer (including negs).

Answer 3

LHS = (tanx*sinx) / (a million-cosx) = [(sinx)^2/cosx] / (a million-cosx) = {[a million-(cosx)^2]/cosx} / (a million-cosx) = {[a million-cosx][a million+cosx]/cosx} / (a million-cosx) = [a million-cosx][a million+cosx]/ [cosx(a million-cosx)] = (a million+cosx)/cosx = (a million/cosx) + a million = a million + a million/cosx = RHS

Answer 4

cosx+1 / cot x = sinx+tanx
cosx + tanx = sinx + tanx
cosx = sinx
x = pi/4 or 5pi/4 radians

Answer 5

is cosx + 1 all in the numerator? If so just break it up into:

cosx/cotx+1/cotx=sinx+tanx
cosx*tanx+1*tanx=sinx+tanx
cosx*(sinx/cosx)+tanx=sinx+tax
sinx+tanx=sinx+tanx

Hope that helped

Answer 6

(cosx+1) / cot x = sinx+tan x
since cot = 1/tan & distributing tan x

cos x * tan x + tan x=sin x + tan x since tan=sin/cos
cos x * sin x .cos x+tan x=sin x + tan x cancel cos x in numerator & denominator
sin x + tan x =sin x +tan x