trigonometry equations

[fiery123]

Prove the following identities.

c) (tanx sinx)/tanx - sinx = (tanx + sinx)/(tanx sinx)

[lintz]

It's been a while since I did similtaneous equations but here goes.

c) (tanx sinx)/tanx - sinx = (tanx + sinx)/(tanx sinx)

tanx sinx = (tanx + sinx)/(tanx sinx) + sinx * tanx
tanx = (tanx + sinx)/(tanx sinx) + sinx - (tanx sinx)
sinx = (tanx + sinx)/(tanx sinx) * tanx - (tanx sinx)

[Glaysher]

Prove the following identities.

c) (tanx sinx)/tanx - sinx = (tanx + sinx)/(tanx sinx)

RHS

(tanx + sinx)/(tanx sinx) = tan x/[tan x sin x] + sinx/[tan x sin x]

= 1/sin x + 1/tan x

= 1/sin x + cos x/sin x

= [1 + cos x]/sin x

LHS

(tanx sinx)/[tanx - sinx] = tan x/[(1/cos x) - 1]

= sin x/[1 - cos x]

= sin x[1 + cos x]/[1 - cos² x]

= sin x[1 + cos x]/sin² x

= [1 + cos x]/sin x

So LHS = RHS

[fiery123]

thanks thanks a lot. sry about forgeting to put brackets around tanx-sinx.