Question

Find the value of sin 20 degree sin 40 degree sin 80 degree

Answer 1

since,sin60=√ 3/2

= √ 3/2( sin20sin40sin80)

=√ 3/2( sin20sin80sin40)

=√ 3/4 [(2sin20sin40)sin80]

on applying [cos(A-B)-cos(A+B) = 2sinAsinB]

we get,

= √ 3/4 (cos20-cos60)sin80 [since,cos(-a)=cosa]

= √ 3/4(cos20sin80-cos60sin80)

= √ 3/8(2sin80cos20-sin80)

= √ 3/8(sin100+sin60-sin80)

= √ 3/8( √ 3/2+sin100-sin80 )

= √ 3/8( √ 3/2+sin(180-80)-sin80 )

= √ 3/8( √ 3/2+sin80-sin80 ) [since,sin(180-a)=sina]

= √ 3/8( √ 3/2)

= 3/16

Answer 2

Answer:

$\frac{\sqrt{3} }{8}$

Step-by-step explanation:

sin 20° sin 40° sin 80°

Use the format -  sin A sin (60-A) sin (60 +A) = $\frac{1}{4}$ sin 3A

sin 20 sin (60-20) sin (60+20) = $\frac{1}{4}$ sin 3×20

$\frac{1}{4}$ sin 60

$\frac{1}{4}$ ×$\frac{\sqrt{3} }{2}$ = $\frac{\sqrt{3} }{8}$

Hence Proved!