Heyy guys..please prove it fast.. SinA.Sin(60⁰-A).Sin(60⁰+A)=1/4Sin3A.
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Step-by-step explanation:
Given, sin(a) * sin(60 - a) * sin(60 + a)
=> sin(a) * (sin(60) cos(a) - sin(a) cos(60)) * (sin(60) cos(a) + sin(a) cos(60))
=> sin(a) * (sin(60)² * cos(a)² - sin(a)² * cos(60)²)
=> sin(a) * ((3/4) * cos(a)² - (1/4) * sin(a)²)
=> (1/4) * sin(a) * (3cos(a)² - sin(a)²)
=> (1/4) * sin(a) * (3 - 3sin(a)² - sin(a)²)
=> (1/4) * (3sin(a) - 4sin(a)³)
=> (1/4) * sin(3a)
Hope it helps!
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