Question

Suppose that sina+sinb = sqrt(5/3) and cosa+cosb=1. What is cos(a-b)?

Answer 1

Consider $$(\sin a+\sin b)^2=5/3,(\cos a+\cos b)^2=1$$ergo$$\sin^2a+\sin^2 b+2\sin a\sin b+\cos^2a+\cos^2b+2\cos a\cos b=5/3+1\\2+2(\sin a\sin b+\cos a\cos b)=5/3+1\\2(\sin a\sin b+\cos a\cos b)=2/3\\2\cos(a-b)=2/3\\\cos(a-b)=1/3$$

Answer 2

Woaahhh!! open my eyes!!! Thank you @oldrin.bataku

Answer 3

notice I used the fact that \(\sin^2a+\cos^2a=\sin^2b+\cos^2b=1\) and also the fact taht \(\cos(a-b)=\sin a\sin b+\cos a\cos b\)

Answer 4

mhmm, thank you!!!! =D