(sinA+cosA)*(sinB-cosB)=sin(b-A)-cos(b+A)

Предыдущий
вопрос Следующий
вопрос

To verify if the given equation is true, we need to expand the left side of the equation and simplify it, and then simplify the right side to see if they are equal.

Expanding the left side of the equation:

(sinA+cosA)(sinB-cosB)
= sinAsinB - sinAcosB + cosAsinB - cosA*cosB
= sin(A+B) - cos(A+B)
= sin(b) - cos(b) (Note: A+B = b and b is a constant)

Therefore, the left side of the equation simplifies to sin(b) - cos(b).

Now, let's simplify the right side of the equation:

sin(b-A) - cos(b+A)
= sin(b-A) - cos(b)cos(A) + sin(b)sin(A)
= sin(b-A) - cos(b)cos(A) + sin(b)sin(A)

We can simplify the right side further, but it is already clear that the left side and right side are not equal. Therefore, the given equation "(sinA+cosA)*(sinB-cosB) = sin(b-A) - cos(b+A)" is not true.