How do you verify $tan (π - x) = - tan x$ $tan (pi - x) = -tanx$ ?

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How do you verify $tan (π - x) = - tan x$ $tan (pi - x) = -tanx$ ?

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Answer 1 · 2016-04-04T13:50:07

Verify trig expression

Explanation:

Two ways.
1. First way. Using the trig unit circle.
tan (pi - x) = - tan x
2. Second way. Apply the identity:
$tan (a - b) = \frac{tan a - tan b}{1 - tan a . tan b}$ $tan (a - b) = (tan a - tan b)/(1 - tan a.tan b)$
$tan (π - x) = \frac{tan π - tan x}{1 - tan (π) . tan x}$ $tan (pi - x) = (tan pi - tan x)/(1 - tan (pi).tan x)$

Since tan (pi) = 0, therefor:
$tan (π - x) = - tan x$ $tan (pi - x) = - tan x$

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How do you verify $tan (π - x) = - tan x$ $tan (pi - x) = -tanx$ ?

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How do you verify tan(π−x)=−tanx tan (pi - x) = -tanx?

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How do you verify $tan (π - x) = - tan x$ $tan (pi - x) = -tanx$ ?