Question

Integrate the following:Ccos%28x%29%20%5C%3A%20%20dx" id="TexFormula1" title=" \displaystyle \int \: \tan(x) \cos(x) \: dx" alt=" \displaystyle \int \: \tan(x) \cos(x) \: dx" align="absmiddle" class="latex-formula">

​

Answer 1

Answer:

$\huge \boxed{\red{ \boxed{ - \cos(x) + C}}}$

Step-by-step explanation:

to understand this

you need to know about:

• integration
• PEMDAS

tips and formulas:

• $\tan( \theta) = \dfrac{ \sin( \theta) }{ \cos( \theta) }$
• $\sf \displaystyle \int \sin(x) \: dx = - \cos(x) + C$

let's solve:

1. $\sf \: rewrite \: \tan( \theta) \: as \: \dfrac{ \sin( \theta) }{ \cos( \theta) } : \\ = \displaystyle \int \: \frac{ \sin(x) }{ \cos(x) } \cos(x) \: dx \\ = \displaystyle \int \: \frac{ \sin(x) }{ \cancel{\cos(x) }} \: \cancel{ \cos(x)} \: dx \\ = \displaystyle \int \: \sin(x) \: dx$
2. $\sf \: use \: the \: formula : \\ \sf \displaystyle - \cos(x)$
3. $\sf add \: constant : \\ - \cos(x) + C$

$\text{And we are done!}$

Answer 2

Answer:

-cosx+c is your answer

Step-by-step explanation:

$\displaystyle \int \: \tan(x) \cos(x) \: dx$

$\displaystyle \int \: \sin \: x \div \cos(x) \times \cos(x) dx$

$\displaystyle \int \: sinx \: dx \\ - \cos(x) + c$