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11 votes
11 votes
Integrate the following:


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



User Randy Dryburgh
by
3.3k points

2 Answers

15 votes
15 votes

Answer:

-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

User SamirChen
by
3.3k points
12 votes
12 votes

Answer:


\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!}

User TeeTracker
by
2.9k points