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Question
The value of sin 50° − sin 70° + sin 10° is equal to
Options
1
0
`1/2`
2
Solution
0
\[\sin50^\circ - \sin70^\circ + \sin10^\circ\]
\[ = 2\sin\left( \frac{50^\circ - 70^\circ}{2} \right) \cos\left( \frac{50^\circ + 70^\circ}{2} \right) + \sin10^\circ \left[ \because \sin A - \sin B = 2\sin\left( \frac{A - B}{2} \right)\cos\left( \frac{A + B}{2} \right) \right]\]
\[ = 2\sin\left( - 10^\circ \right) \cos60^\circ + \sin10^\circ\]
\[ = 2 \times \frac{1}{2}\sin\left( - 10^\circ \right) + \sin10^\circ\]
\[ = - \sin10^\circ + \sin10^\circ\]
\[ = 0\]
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