The value of 50^ - 70^ + 10^ is equal to - Vidyadip

MCQ

The value of $\sin50^\circ-\sin70^\circ+\sin10^\circ$is equal to

A
$1$
✓
$0$
C
$\frac{1}{2}$
D
$2$

✓

Answer

Correct option: B.

$0$

$\sin50^\circ-\sin70^\circ+\sin10^\circ$
$=\ 2\sin\Big(\frac{50^\circ-70^\circ}{2}\Big)\cos\Big(\frac{50^\circ+70^\circ}{2}\Big)+\sin10^\circ$
$\Big[\because\ \sin\text{A}-\sin\text{B}=2\sin\Big(\frac{\text{A}-\text{B}}{2}\Big)\cos\Big(\frac{\text{A}+\text{B}}{2}\Big)\Big]$
$=\ 2\sin(-10^\circ)\cos60^\circ+\sin10^\circ$
$=\ 2\times\frac{1}{2}\sin(-10^\circ)+\sin10^\circ$
$=\ -\sin10^\circ+\sin10^\circ$
$=\ 0$

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