# How to simplify tanx/tanx +cotx ?

Krishnamurthy

tan x / tan x + cot x = 1 + cot x

Captain Matticus, LandPiratesInc: Assuming you meant

Assuming you meant: tan(x) / (tan(x) + cot(x)) => tan(x) / (tan(x) + 1/tan(x)) => tan(x) / ((tan(x)^2 + 1) / tan(x)) => tan(x) * tan(x) / (1 + tan(x)^2) => tan(x)^2 / sec(x)^2 => (sin(x)^2 / cos(x)^2) / sec(x)^2 => sin(x)^2 / (cos(x)^2 * sec(x)^2) => sin(x)^2 / 1 => sin(x)^2 There you go. You can reduce the powers, too sin(x)^2 => (1/2) * (1 - cos(2x))

Pope

tan(x)/tan(x) + cot(x) = 1 + cot(x), where x ≠ kπ/2 for any integer k For any other x the expression is undefined.

alex

tanx/tanx +cotx = 1 + cotx

Como

Will assume that presentation is incorrect and should be :- tan x / ( tan x + cot x ) tan x ---------------------- tan x + 1/tan x tan²x ------------------- tan²x + 1 tan²x ---------- sec²x tan²x cos²x = sin²x

MyRank

tanx / (tanx + cotx) (Sinx/cosx) / (sinx / cosx) + cosx / sinx (sinx / cosx) / sin²x + cos²x) / (cosx sinx) sin²x / 1 = sin²x.

Priyankka

Sin^2 x

Philip

f = t/[t + 1/t] = t^2/[1 + t^2] = 1/[1+ c^2/s^2] =1/[(s^2+c^2)/s^2] = s^2,where {s,c} = {sinx,cosx}.

khalil

the bottom tanx + cotx = sinx/cosx + cosx/sinx = 1/(sinx cosx) tanx ( sinx cosx ) = sin²(x) ◄◄◄

Steve A

tanx / (tanx + cotx) (sinx/cosx) / ((sinx/cosx) + (cosx/sinx)) (sinx/cosx) / ((sin^2x + cos^2x)/(sinx*cosx) (sinx/cosx) / (1/(sinx*cosx)) sinx(sinx*cosx)/cosx sin^2x