What is sin/cos + cos/sin, and why?

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Answer 1 · 2015-04-15T17:47:46

The problem here is "how far back do we need to go?" when we try to explain "why?"

Assuming that the following identities are known:
$sin^2(x)+cos^2(x) = 1$
and
$sin(2x) = 2sin(x)cos(x)$

$(sin(x))/(cos(x)) + (cos(x))/(sin(x))$

$= (sin(x))/(cos(x)) * (sin(x))/(sin(x)) + (cos(x))/(sin(x)) * (cos(x))/(cos(x))$

$= (sin^2(x)+cos^2(x))/cos(x)sin(x)$

$= 1/(cos(x)sin(x))$

or
$= 2/sin(2x)$