Cos (arcsin1/3 -arccos2 /3)​

соs(a - b) = cos(a)*cos(b)  + sin(a)*sin(b)

sin(arccos(x)) = √(1 - x²)   |x|<=1

cos(arcsin(x)) = √(1 - x²)   |x|<=1

cos(arcsin(1/3) - arccos (2/3)) = cos(arcsin(1/3))*cos(arccos(2/3)) + sin(arcsin(1/3))*sin(arccos(2/3)) = √(1 - 1/3²)*2/3 + 1/3*√(1 - (2/3)²) = √8/3*2/3 + 1/3*√5/3 = 4√2/9 + √5/9 = (4√2 + √5)/9

Объяснение:

1/3=x; 2/3=y

сos(arcsinx-arccosy)=cos(arcsinx)×cos(arccosy)+sin(arcsinx)×sin(arccosy)

cos(arcsinx)=√(1-x²)=; cos(arccosy)=y=;  sin(arcsinx)=x=;   sin(arccosy)=√(1-y²)=

cos (arcsin1/3 -arccos2 /3)=