Question

if sin(π/12)=1/2√(a - √b), then, by using a half - angle formula, find a =, b =. question help: d post to forum

Explanation:

Step1: Recall the half - angle formula for sine

The half - angle formula for $\sin\frac{\alpha}{2}=\pm\sqrt{\frac{1 - \cos\alpha}{2}}$. Let $\alpha=\frac{\pi}{6}$, then $\frac{\alpha}{2}=\frac{\pi}{12}$.

Step2: Substitute $\alpha=\frac{\pi}{6}$ into the formula

We know that $\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}$. So $\sin\frac{\pi}{12}=\sqrt{\frac{1-\cos\frac{\pi}{6}}{2}}=\sqrt{\frac{1 - \frac{\sqrt{3}}{2}}{2}}$.

Step3: Simplify the expression

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Answer:

$A = 2$, $B = 3$