Understanding the False Statement (tan X)(cos X) = (sin X) in Trigonometry

[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?

 

[NateTG]

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?

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

 

[ComputerGeek]

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

$$tan\frac{\pi}{2}$$ 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.