Question

sin pi/4 sin pi/6= 1/2(_____ pi/12-cos 5pi/12)

Answer 1

Answer: sin pi/4 sin pi/6 = 1/2(cos pi/12 - cos 5pi/12)

correct on apex

Answer 2

Answer:

$sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})$

Step-by-step explanation:

We are given that

$sin\frac{\pi}{4} sin\frac{\pi}{6}$

We have to correct value in blank space.

We know that identity

$sin xsiny=\frac{cos(x-y)-cos(x+y)}{2}$

Using this identity

$sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{cos(\frac{\pi}{4}-\frac{\pi}{6})-cos(\frac{\pi}{4}+\frac{\pi}{6})}{2}$

$sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{cos(\frac{3\pi-2\pi}{12}-cos(\frac{3\pi+2\pi}{12})}{2}$

$sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})$

Answer:$sin\frac{\pi}{4}sin\frac{\pi}{6}=\frac{1}{2}(cos\frac{\pi}{12}-cos\frac{5\pi}{12})$