Find the antiderivative of f(x)=cos2x/(sin^2x)*(cos^2x).

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have the function f(x) = cos 2x /(sin x)^2*(cos x)^2

cos 2x = (cos x)^2 - ( sin x)^2

=> cos 2x /(sin x)^2*(cos x)^2

=> [(cos x)^2 - ( sin x)^2] / (sin x)^2*(cos x)^2

=> 1/ (sin x)^2 - 1/ (cos x)^2

=> (cosec x)^2 - (sec x)^2

So, Int [ f(x)]

=> Int [ (cosec x)^2 - (sec x)^2 dx]

=> Int [(cosec x)^2 dx] - Int [(sec x)^2 dx]

=> - tan x  - cot x + C

Therefore the required antiderivative of f(x)=cos2x/(sin^2x)*(cos^2x) = -tan x  - cot x + C

Approved by eNotes Editorial Team

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial