the exact value of sin(5π/12) is: a. 0.02. b. (√2(√3 - 1))/4. c. 0.97. d. (√2(√3 + 1))/4.

Answer:

D. $\frac{\sqrt{2}(\sqrt{3}+1)}{4}$

Explanation:

Step1: Rewrite the angle

We know that $\frac{5\pi}{12}=\frac{\pi}{4}+\frac{\pi}{6}$.

Step2: Use the sum - formula for sine

The formula for $\sin(A + B)=\sin A\cos B+\cos A\sin B$. Here $A=\frac{\pi}{4}$ and $B = \frac{\pi}{6}$. $\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}$, $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$, $\sin\frac{\pi}{6}=\frac{1}{2}$, $\cos\frac{\pi}{6}=\frac{\sqrt{3}}{2}$.

Step3: Substitute the values

$\sin(\frac{\pi}{4}+\frac{\pi}{6})=\sin\frac{\pi}{4}\cos\frac{\pi}{6}+\cos\frac{\pi}{4}\sin\frac{\pi}{6}=\frac{\sqrt{2}}{2}\times\frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}\times\frac{1}{2}=\frac{\sqrt{6}+\sqrt{2}}{4}=\frac{\sqrt{2}(\sqrt{3} + 1)}{4}$.