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.