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State whether the following are true or false. Justify your answer. sin (A + B) = sin A + sin B.

 State whether the following are true or false. Justify your answer. 
 
 sin (A + B) = sin A + sin B.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

The solution isFalse.

Justification:
Let us take an example of A = 30° and B = 60°, then
Substitute the values in the sin (A + B) formula,
we get sin (A + B) = sin (30° + 60°)
= sin 90°
= 1
and,
sin A + sin B = sin 30° + sin 60°

= 1/2+ √3/2
= 1+√3/2
Since the values obtained are not equal, the solution is false.

Thanks

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