Question

is it right to say that sin(A+B)=sinA+sinB

Answer 1

Let A be 30° 
and B be 60°

   Sin(A+B)
= Sin(30°+60°)
= Sin90° 
= 1 ---------------(1)

   SinA + SinB
= Sin30° + Sin60°
= 1/2 + (√3)/2
= (1+√3)/2  -----------(2)

(1) is not equal to (2)
∴ It is not right to say that Sin(A+B)= Sin A + Sin B

Answer 2

Sin(A+B) = SinA+SinB

Let A = 30° and B = 60°

Sin(30°+60°) = Sin30°+Sin60°

$sin {90}^{0} = \frac{1}{2} + \frac{ \sqrt{3} }{2}$

$1 = \frac{1}{2} + \frac{ \sqrt{ 3} }{2}$

$1 \: is \: not \: equal \: to \: \frac{1 + \sqrt{3} }{2}$

L.H.S is not equal to R.H.S

Therefore Sin(A+B) is not equal to SinA+SinB.

Consider,

Sin(A+B)=SinA+SinB

Let A = 0° and B=30°

Sin(0°+30°) = SinA+SinB

Sin30° = Sin0°+Sin30°

Sin30° = 0+1/2

1/2 = 1/2

L.H.S = R.H.S

Therefore Sin(A+B) = SinA+SinB

Therefore Sin(A+B) = SinA+SinB when either A is 0° or B is 0°.