Question

The value of sin 50° − sin 70° + sin 10° is equal to
(a) 1
(b) 0
(c) 1/2
(d) 2

Answer 1

(b) 0

$$\begin{gathered} \sin 50°-\sin 70°+\sin 10° \\ =2\sin \left(\frac{50°-70°}{2}\right)\cos \left(\frac{50°+70°}{2}\right)+\sin 10°\left[\because \sin A-\sin B=2\sin \left(\frac{A-B}{2}\right)\cos \left({\displaystyle \frac{A+B}{2}}\right)\right] \\ =2\sin \left(-10°\right)\cos 60°+\sin 10° \\ =2\times \frac{1}{2}\sin \left(-10°\right)+\sin 10° \\ =-\sin 10°+\sin 10° \\ =0 \end{gathered}$$