How do you simplify $\frac{tan x}{sec x - cos x}$ $tan x/ (sec x - cos x)$ ?

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How do you simplify $\frac{tan x}{sec x - cos x}$ $tan x/ (sec x - cos x)$ ?

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Answer 1 · 2018-06-02T16:47:19

$\frac{tan x}{sec x - cos x} = csc x$ $tanx/(secx-cosx)=cscx$

Explanation:

$\frac{tan x}{sec x - cos x} = ?$ $tanx/(secx-cosx)=?$
$tan x = \frac{sin x}{cos x}; sec x = \frac{1}{cos x}$ $tanx=sinx/cosx; secx=1/cosx$
$\frac{tan x}{sec x - cos x} = \frac{\frac{sin x}{cos x}}{\frac{1}{cos x} - cos x}$ $tanx/(secx-cosx)=(sinx/cosx)/(1/cosx-cosx)$
Multiplying numerator and denominator by cosx
$= \frac{sin x}{1 - {cos}^{2} x}$ $=sinx/(1-cos^2x)$
$1 - {cos}^{2} x = {sin}^{2} x$ $1-cos^2x=sin^2x$
$\frac{tan x}{sec x - cos x} = \frac{sin x}{{sin}^{2} x} = \frac{1}{sin x} = csc x$ $tanx/(secx-cosx)=sinx/sin^2x=1/sinx=cscx$

$\frac{tan x}{sec x - cos x} = csc x$ $tanx/(secx-cosx)=cscx$

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How do you simplify $\frac{tan x}{sec x - cos x}$ $tan x/ (sec x - cos x)$ ?

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