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State whether the following are true or false. Justify your answer. sin (A + B) = sin A + sin B - CBSE Class 10 - Mathematics

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Question

State whether the following is true or false. Justify your answer.

sin (A + B) = sin A + sin B

  • True

  • False

Solution

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.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 8: Introduction to Trigonometry
Ex. 8.20 | Q: 4.1 | Page no. 187
Solution State whether the following are true or false. Justify your answer. sin (A + B) = sin A + sin B Concept: Trigonometric Ratios of Some Specific Angles.
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