Question

Integrate the following:


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

​

Answer 1

-cosx+c is your answer

Explanation:

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

`\displaystyle \int \: \sin \: x / \cos(x) * \cos(x) dx`

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

Answer 2

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

Explanation:

to understand this

you need to know about:

• integration
• PEMDAS

tips and formulas:

• 
  `\tan( \theta) = ( \sin( \theta) )/( \cos( \theta) )`
• 
  `\sf \displaystyle \int \sin(x) \: dx = - \cos(x) + C`

let's solve:

1. 
   `\sf \: rewrite \: \tan( \theta) \: as \: ( \sin( \theta) )/( \cos( \theta) ) : \\ = \displaystyle \int \: ( \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!}`