Given cot x=1/5, what is the value cos^2 x?

Expert Answers

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

We have cot x=  1/5. We need the value of (cos x)^2

(sin x)^2 + (cos x)^2 = 1

divide all terms by (sin x)^2

=> 1 + (cot x)^2 = 1/(sin x)^2

substitute cot x = 1/5

=> 1 + (1/5)^2 = 1/(sin x)^2

=> 1/(sin x)^2 = 1 + 1/25

=> 1/(sin x)^2 = 26/25

=> (sin x)^2 = 25/26

=> 1 - (cos x)^2 = (25/26)

=> (cos x)^2 = (1 - 25/26)

=> (cos x)^2 = (1/26)

The value of (cos x)^2 = 1/26

Approved by eNotes Editorial Team
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