Prove the following identities.
c) (tanx sinx)/tanx - sinx = (tanx + sinx)/(tanx sinx)
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Prove the following identities.
c) (tanx sinx)/tanx - sinx = (tanx + sinx)/(tanx sinx)
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)
RHSQuote:
Originally Posted by fiery123
(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
thanks thanks a lot. sry about forgeting to put brackets around tanx-sinx.