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Question
State whether the following is true or false. Justify your answer.
sin (A + B) = sin A + sin B
Options
True
False
Solution
This statement is False.
Explanation:
sin (A + B) = sin A + sin B
Let A = 30° and B = 60°
sin (A + B) = sin (30° + 60°)
= sin 90°
= 1
sin A + sin B = sin 30° + sin 60°
= `1/2 + (sqrt3)/2`
= `(1+sqrt3)/2`
Clearly, sin (A + B) ≠ sin A + sin B
Hence, the given statement is false.
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