Question

1) sin(a+B)- sin(a-B);

Answer 1

Объяснение:

<var>sin(a+b)+sin(a−b)=sinA∗cosB+cosA∗sinB+sinA∗cosB−cosAsinB=2sinA∗cosB</var>

Answer 2

To simplify the expression $\sin(a+B) - \sin(a-B)$, you can use the trigonometric identity for the difference of two sines:

$\sin(A) - \sin(B) = 2\sin\left(\frac{A-B}{2}\right)\cos\left(\frac{A+B}{2}\right)$

In your expression, $A = a + B$ and $B = a - B$, so:

$\sin(a+B) - \sin(a-B) = 2\sin\left(\frac{(a+B)-(a-B)}{2}\right)\cos\left(\frac{(a+B)+(a-B)}{2}\right)$

Now, simplify further:

$2\sin\left(\frac{2B}{2}\right)\cos\left(\frac{2a}{2}\right)$

$2\sin(B)\cos(a)$

So, the simplified expression is $2\sin(B)\cos(a)$.