Question

Value of cos(a-b) if sina + sinb = x and cosa + cosb =y

Answer 1

sina + sinb = x

or, sin^2a + sin^2b + 2sinasinb = x^2

................ (i)

cosa + cosb = y

or, cos^2a + cos^2b + 2cosacosb = y^2

................(ii)

(i)+(ii) , we get ,

( sin^2a + cos^2a ) + ( sin^2b + cos^2b ) +

2(cosacosb + sinasinb) = x^2 + y^2

or, 2 + 2(cosacosb + sinasinb) = x^2 + y^2

or, cosacosb + sinasinb = ( x^2 + y^2 - 2 ) / 2

cos(a-b)

=cosacosb + sinasinb

= ( x^2 + y^2 - 2 ) / 2