Question

Evalute: rn sin20.sin40.sin80

Answer 1

Hi ,
___________
SinASin( 60 - A ) sin ( 60 + A )

=SinA [(Sin60cosA- cos60sinA)

(Sin60cosA + cos60sinA)]

=SinA [ (Sin60cosA)² - (cos60sinA)² ]

=SinA [ (√3/2×cosA )² - ( 1/2 × sinA )² ]

=SinA(3 Cos² A )/4 - ( sin² A) / 4

= 1/4×SinA [ 3cos² A - sin² A]

= 1/4 × SinA[3( 1- sin²A) - sin² A ]

= (SinA)/4[3 - 3sin² A - sin² A ]

= ( SinA)/4 [ 3- 4sin² A]

= [ 3sinA - 4sin³ A ]/4

=( Sin3A)/4 ------( 1 )
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Here A = 20,

Sin 20sin40sin80

= Sin20sin(60-20)sin(60+20)

=[ Sin (3×20)]/4 from ( 1 )

= (Sin60)/4

= ( √3/2 ) / 4

= √3 / 8

I hope this helps you.

:)

Answer 2

Hope it helps you all

!