# Short trig question

1. Dec 7, 2005

### dnt

how is (tan X)(cos X) = (sin X) false?

tan is sin/cos so when you multiply by cos, you get sin...yet the answer i was given was false? how so?

2. Dec 7, 2005

### NateTG

Well,
$$\sin \frac{\pi}{2}=1$$
while
$$\tan \frac{\pi}{2}$$
is undefined.

3. Dec 8, 2005

### ComputerGeek

$$tan\frac{\pi}{2}$$ is undefined because $$cos\frac{\pi}{2}$$ is zero.
but that did not answer his question.
The answer is that $$(tan x)(cos x)$$ is not equal to $$sin x$$ because when $$tan x$$ is undefined, the denominator of the trigonometric fraction $$\frac{sin x}{cos x}$$ is zero and when you have a zero denominator, multiplying by zero in the numerator still results in an undefined result.

Last edited: Dec 8, 2005