Question

Heya Friends !!

Prove that. : -
sin π/18 × sin 5π/18 × sin 7π/18 =1/8

Answer 1

Hey;
ANSWER TO YOUR QUESTION IS:-

sin(pi/18)*sin(5pi/18)*sin(7pi/18)= 

=sin10xsin50xsin70

=-1/2(cos60-cos40)sin70

==-1/2(1/2-cos40)sin70

=-1/4(1-2cos40)sin70 

=-1/4(sin70-2cos40sin70) 
-1/4(sin70-2sin50sin70) 

=-1/4(sin70+(cos120-cos20)

=-1/4(sin70-cos20-1/2)
 
=-1/4(sin70-sin70-1/2)

=-1/4(-1/2)

=1/8 =ANSWER

HOPE IT HELPS:-))

Answer 2

Answer:

To prove: sin π/18 × sin 5π/18 × sin 7π/18 =1/8

We know that ,

π/18 = 10° , 5π/18 = 50° and 7π/18 = 70°

Consider,

LHS

= sin π/18 × sin 5π/18 × sin 7π/18

= sin 10 × sin 50 × sin 70

= -1/2 ( cos (10+50) - cos (50-10) ) × sin 70

= -1/2 ( cos 60 - cos 40 ) × sin 70

= -1/2 ( 1/2 - cos 40 ) × sin 70

= -1/4 ( 1 - 2cos 40 ) × sin 70

= -1/4 ( sin 70 - 2 cos 40 × sin 70 )

= -1/4 ( sin 70 - 2 sin ( 90 - 50 ) × sin 70 )

= -1/4 ( sin 70 - 2 sin 50 × sin 70 )

= -1/4 ( sin 70 + ( cos( 50 + 70 ) - cos( 70 - 50) ) )

= -1/4 ( sin 70 + ( cos 120 - cos 20 ) )

= -1/4 ( sin 70 + ( cos 120 - sin ( 90 - 70 ) ) )

= -1/4 ( sin 70 + ( cos 120 - sin 70 ) )

= -1/4 ( sin 70 + cos 120 - sin 70 )

= -1/4 ( cos 120 )

= -1/4 ( -1/2 )

= 1/8

= RHS