Question

Aratati ca pentru orice x,y apartinand lui R avem :
a)cos(x+y)*cos(x-y)=cos^2 x-sin^2 y
b)cos(x+y)+sin(x-y)=sin x*cos x- sin y*cos y

Answer 1

[tex]a)\:cos(x+y)\cdot cos(x-y)=(\cos{x}\cos{y}-\sin{x}\sin{y})(\cos{x}\cos{y}\\ +\sin{y}\sin{x})=\cos^2{x}\cos^2{y}-\sin^2{x}\sin^2{y}=\\ =\cos^2{x}(1-\sin{^2{y})-\sin^2{y}(1-\cos^2{x})= \\ =\cos^2{x}-\cos^2{x}\cdot\sin{^2{y}-\sin^2{y}+\sin^2{y}\cdot\cos^2{x}=\\ =\cos^2{x}-\sin{^2{y}[/tex]
La b) ai scris corect?