`cos(x+y)*cos(x-y)=cos^2x-sin^2y` ``

Expert Answers

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

`cos(x+y)*cos(x-y)= cos^2 x - sin^2 x`

`` We will use trigonometric identities to prove the identities.

We know that:

`cosa*cosb= (1/2)(cos(a-b)+cos(a+b)) `

`==gt cos(x+y)*cos(x-y)= (1/2)(cos(x+y-x+y)+cos(x+y+x-y)) `

`==gt cos(x+y)*cos(x-y)= (1/2)(cos(2y) + cos(2x)) `

`==gt cos(x+y)*cos(x-y)= (1/2)((1-2sin^2 y)+(2cos^2x -1)) `

`==gt cos(x+y)*cos(x-y)= (1/2)( 2cos^2 x - 2sin^2y +1 -1) `

`==gt cos(x+y)*cos(x-y)= (1/2)2(cos^2 x-sin^2y) `

`==gt cos(x+y)*cos(x-y)= cos^2 x - sin^2 y.`


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