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Trig identity proof

Prove that cosecx/cotx + tanx = cosx

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

Made denominators the same and added, ended up getting 1/sin^2xcosx

Help please

Reply 1

RDKGames

Study Forum Helper

Original post by G.Y

Prove that cosecx/cotx + tanx = cosx

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

Made denominators the same and added, ended up getting 1/sin^2xcosx

Help please

OK, took me a while to notice that you didnt format your original equation correctly and actually meant the second one.

Anyway,

\dfrac{\csc x}{ \cot x + \tan x} = \dfrac{1}{\sin x (\cot x + \tan x)}

so you made an error there.

Reply 2

G.Y

Original post by RDKGames

OK, took me a while to notice that you didnt format your original equation correctly and actually meant the second one.

Anyway,

\dfrac{\csc x}{ \cot x + \tan x} = \dfrac{1}{\sin x (\cot x + \tan x)}

so you made an error there.

I don't understand

Reply 3

samb216

sin = s
cos = c
cot = cos/sin
tan = sin/cos

(1/s) / [(c/s) + (s/c)] = LHS

=(1/s) / (c^2/sc + s^2 / sc)
=(1/s) / [(c^2 + s^2) / sc]
**c^2 + s^2 = 1**
**diving by a fraction is the same as multiplying by the reciprocal**
=1/s * (sc / 1)
=sc / s
=c
= RHS