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# The value of sin 50° − sin 70° + sin 10° is equal to

Question:

The value of sin 50° − sin 70° + sin 10° is equal to

(a) 1

(b) 0

(c) 1/2

(d) 2

Solution:

(b) 0

$\sin 50^{\circ}-\sin 70^{\circ}+\sin 10^{\circ}$

$=2 \sin \left(\frac{50^{\circ}-70^{\circ}}{2}\right) \cos \left(\frac{50^{\circ}+70^{\circ}}{2}\right)+\sin 10^{\circ} \quad\left[\because \sin A-\sin B=2 \sin \left(\frac{A-B}{2}\right) \cos \left(\frac{A+B}{2}\right)\right]$

$=2 \sin \left(-10^{\circ}\right) \cos 60^{\circ}+\sin 10^{\circ}$

$=2 \times \frac{1}{2} \sin \left(-10^{\circ}\right)+\sin 10^{\circ}$

$=-\sin 10^{\circ}+\sin 10^{\circ}$

$=0$