Question

prove that Sin(A+B) =SinA+SinB​

Answer 1

Answer:

This is the wrong identity

sin(A+B) = sinAcosB+cosAsinB

is the correct identity

hope it helps!!

Answer 2

$\sf\huge\bold{Answer:}$

Given :

⟶Sin(A+B) =SinA+SinB

To prove :

LHS = RHS

Solution :

As we know ,

⇒ sin(A+B) = sinAcosB+sinBcosA

So,if cos function can be eliminated from RHS,then we will get the required result.

To eliminate cos function,let us take some cases for values of A and B

For RHS

$\fbox{Case 1 :}$When A is 0°

⟶sin0°×cosB+sinB×cos0°

⟶0 + sinB × 1

⟶sinB

$\fbox{Case 2 :}$ When A is 90°

⟶sin90°×cosB+sinB×cos90°

⟶cosB×1+0

⟶cosB

$\fbox{Case 3 :}$When B is 0°

⟶sinA×cos0°+sin0°×cosA

⟶sinA×1+0

⟶sinA

$\fbox{Case 4 :}$When B is 90°

⟶sinA×cos90°+sin90°×cosA

⟶0+1×cosA

⟶cosA

It can be easily seen that in none of these cases,Sin(A+B) =SinA+SinB

Hence this is not right relation between functions.