How do you simplify $(sec x - cos x) / tan x$ ?

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Answer 1 · 2015-08-22T15:50:37

$sinx$

This can also be proven by showing that $secx-cosx = (tanx)(sinx)$ and then dividing both sides by $tanx$

Let's start by breaking down some terms. In my opinion, you have to kind of play around with trig stuff to get it to break down right.

$secx=1/cosx=tanx/sinx$

So,

$(secx-cosx)/tanx = secx/tanx - cosx/tanx = (tanx/sinx)/tanx - cosx/tanx$

$=1/sinx - cosx/tanx$

Tangent = sine/cosine, so the reciprocal of the tangent = cosine/sine

$= 1/sinx - cos^2x/sinx = (1-cos^2x)/sinx$

Since $sin^2x+cos^2x=1$ , that means $cos^2x=1-sin^2x$

$= (1-(1-sin^2x))/sinx = (1 - 1 + sin^2x)/sinx = sin^2x/sinx = sinx$

Final Answer

How do you simplify (sec x - cos x) / tan x(sec x - cos x) / tan x?