Question

Sin 20 sin 40 sin 80 prove that root 2 by 8

Answer 1

here's the answer...

Sin(20)sin(40) = (1/2)[cos(20) - cos(60)] 
                       =sin(20)sin(40)sin(80) 
                       = (1/2)[cos(20) - cos(60)]sin(80) 
                       = (1/2)[cos(20)sin(80) - cos(60)sin(80)] 
                       = (1/2)[(1/2)(sin(100)+sin(60)) - (1/2)(sin(140)+sin(20))] 
                       = (1/4)[sin(80) + sin(60) - sin(40) - sin(20)] 
                       = (1/4)sin(60), since sin(80) - sin(40) - sin(20) = sin(60+20) -                              sin(60-20) - sin(20) = 2cos(60)sin(20) - sin(20) = 0 
                       = √3/8
it is not by 2/8 it is 3/8

I think this is the answer...

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