How do you prove $\frac{1 + tan x}{1 + cot x} = tan x$ $(1+tanx)/(1+cotx) = tanx$ ?

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Answer 1 · 2016-05-13T15:30:23

Left Side: $= \frac{1 + tan x}{1 + cot x}$ $=(1+tanx)/(1+cotx)$

$= \frac{1 + \frac{sin x}{cos x}}{1 + \frac{cos x}{sin x}}$ $=(1+sinx/cosx)/(1+cosx/sinx$

$= \frac{\frac{cos x + sin x}{cos x}}{\frac{sin x + cos x}{sin x}}$ $=((cosx+sinx)/cosx)/((sinx+cosx)/sinx)$

$= (\frac{cos x + sin x}{cos x}) \cdot (\frac{sin x}{cos x + sin x})$ $=((cosx+sinx)/cosx) *(sinx/(cosx+sinx))$

$= \frac{sin x}{cos x}$ $=sinx/cosx$

$= tan x$ $=tanx$

$=$ $=$ Right Side

How do you prove 1+tanx1+cotx=tanx(1+tanx)/(1+cotx) = tanx?