Question:
Using the formula, $\sin A=\sqrt{\frac{1-\cos 2 A}{2}}$, find the value of $\sin 30^{\circ}$, it being given that $\cos 60^{\circ}=\frac{1}{2}$.
Solution:
A = 30o
⇒ 2A = 2
By substituting the value of the given T-ratio, we get:
$\sin A=\sqrt{\frac{1-\cos 2 A}{2}}$
$\Rightarrow \sin 30^{\circ}=\sqrt{\frac{1-\cos 60^{\circ}}{2}}=\sqrt{\frac{1-\frac{1}{2}}{2}}=\sqrt{\frac{\frac{1}{2}}{2}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$
$\therefore \sin 30^{\circ}=\frac{1}{2}$
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