Question

Raju said that sin(A+B)=sinA+sinB.do you agree with his statement? Justify your answer​

Answer 1

Answer:

yes, I agree

justification is given above

Answer 2

Answer:

No, Raju's statement is not right as both the expressions have different values.

Step-by-step explanation:

We know that there is a trigonometric identity for calculating the sine of sum of two angles, $A$ and $B$, i.e., $sin(A+B)$.

The identity is as follows:

$sin(A+B) = sinA.cosB+cosA.sinB$

Also, the trigonometric identity for the sum of sine of two angles, $A$ and $B$, i.e., $sinA+sinB$.

The identity is as follows:

$sinA+sinB=2.sin(\frac{A+B}{2}).cos(\frac{A-B}{2})$

Now, we are given in the question that:

$sin(A+B)=sinA+sinB$

Using these identities, we get:

$sinA.cosB+cosA.sinB\ne 2.sin(\frac{A+B}{2}).cos(\frac{A-B}{2})$

Thus, Raju's statement is wrong as the two used expressions have different values.