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
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
Already a member? Log in here.
Are you a teacher? Sign up now