(sinx-siny)^2+(cosx-cosy)^2=4sin^2 x-y/2 (sina+sinb)^2+(cosa+cosb)^2=4cos a-b/2 Докажите...

Question

(sinx-siny)^2+(cosx-cosy)^2=4sin^2 x-y/2
(sina+sinb)^2+(cosa+cosb)^2=4cos a-b/2 Докажите тождество

Answer 1

(sina+sinb)^2+(cosa+cosb) ^2 = sin^2(a) + sin^2(b) + 2sin(a)sin(b) + cos^2(a) + cos^2(b) + 2cos(a)cos(b) = (sin^2(a) + cos^2(a)) + (sin^2(b) + cos^2(b)) + 2(sin(a)sin(b) + cos(a)cos(b)) = 1 + 1 +2cos(a-b) = 2 + 2cos(a-b) = 2(1 + cos(a-b)) = 4(1 + cos(a-b)) / 2 = 4cos^2((a-b)/2)