How to state the equivalent expression for cosxtanx?

Nov 19, 2017

$\sin \left(x\right)$

Explanation:

One of our most important trig identities is:

$\tan \left(x\right) = \sin \frac{x}{\cos} \left(x\right)$

Hence, we can rewrite the expression above as:

$\cos \left(x\right) \left[\sin \frac{x}{\cos} \left(x\right)\right]$

Now, the cosines cancel out, so we're just left with:

$\textcolor{red}{\cancel{\cos \left(x\right)}} \left[\sin \frac{x}{\textcolor{red}{\cancel{\cos \left(x\right)}}}\right]$

$\implies \sin \left(x\right)$

Hope that helped :)