Question

sin10.sin50.sin70=1/8

Answer 1

sin10sin50sin70= sin(90-80)sin(90-40)sin(90-20) =
cos80cos40cos20/1 => multiply and divide by 2sin20=> then we get (sin2A=2sinAcosA) =>
2sin20cos20cos40cos80/2sin20=> sin40cos40cos80/2sin20=> multiply and divide by 2=> 2sin40cos40cos80/4sin20=> sin80cos80/4sin20 => multiply and divide by 2,we get 2sin80cos80/8sin20=> sin160/sin20
(sin(180-A)=sinA) => sin20/8sin20=> 1/8 . Hence proved .Hope it helps you...
Mark me as Brainliest.

Answer 2

Converting all sine functions in cosine.
Taking L. H. S.
cos(90-10) cos(90-50) cos (90-70)
=>cos80 cos40 cos20
=>cos20 cos40 cos80
Applying cosine theorm
=>sin 2³ 20/2³sin20
=>1/8(sin8x20/sin20 )
=>1/8(sin160/sin20)
=>1/8[sin(180-20)/sin20]
=>1/8(sin20/sin20)
=> 1/8 X 1
=>1/8 =R. H. S.

HOPE IT HELPS YOU
^_^