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Alexus [3.1K]
3 years ago
12

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

Mathematics
2 answers:
jonny [76]3 years ago
7 0

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

correct on apex

Vanyuwa [196]3 years ago
3 0

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})

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