Calculate cos(a-b) Given that sina + sinb =1 and cosa + cosb = 1/2 calculate cos(a-b)

Expert Answers

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

The value of cos (a - b) has to be found given that sin a + sin b = 1 and cos a + cos b = 1/2.

cos (a - b) = cos a* cos b + sin a * sin b

sin a + sin b = 1

square both the sides

=> (sin a)^2 + (sin b)^2 + 2*sin a * sin b = 1 ...(1)

cos a + cos b = 1/2

square both the sides

(cos a)^2 + (cos b)^2 + 2*cos a* cos b = 1/4 ...(2)

(2) + (1)

=> (cos a)^2 + (cos b)^2 + 2*cos a* cos b  + (sin a)^2 + (sin b)^2 + 2*sin a * sin b = 1 + 1/4

use the property (sin a)^2 + (cos a)^2 = 1

=> 2 + 2*cos a* cos b  + 2*sin a * sin b = 5/4

=> 2*cos a* cos b  + 2*sin a * sin b = 5/4 - 2

=> cos a* cos b  + sin a * sin b = 5/8 - 1

=> cos (a - b) = -3/8

The value of cos (a - b) = -3/8

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