1. ## Trigonometric Quotient Identities

I wouldn't normally ask, but I'm trying to make a chart of trigonometric identities (beyond the most fundamental) so that I don't have to calculate the same things over and over.

So, tan x * cos x = sin x

But, what is tan/cos? I thought it was sin/cos^2, but I'm not sure.

2. Originally Posted by Picatta
I wouldn't normally ask, but I'm trying to make a chart of trigonometric identities (beyond the most fundamental) so that I don't have to calculate the same things over and over.

So, tan x * cos x = sin x

But, what is tan/cos? I thought it was sin/cos^2, but I'm not sure.
$\displaystyle tan x = \frac{sin x}{cos x}$

$\displaystyle tan x \times cos x = sin x$

Now we want to get rid of that $\displaystyle cos x$ and we also want $\displaystyle cos x$ in the denominator. Divinding by $\displaystyle cos^2 x$ should fix that. Recall that we have to do the same thing to both sides of the equation.

$\displaystyle \frac{tan x}{cos x} = \frac{sin x}{cos^2 x}$

So you were correct!

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EDIT: An even easier way...

$\displaystyle tan x = \frac{sin x}{cos x}$

Divide by cos $\displaystyle x$ both sides.

$\displaystyle \frac{tan x}{cos x} = \frac{sin x}{cos^2 x}$