NIMCET 2014 Question Paper with solutions

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Question : 43 of 120

Marks: +1, -0

The value of sin 20° sin 40° sin 80° is

$1/2$
$√3/2$
$√3/8$
$1/8$

Solution:

We have,
sin20°sin40°sin80°
= sin20°sin(60° -20°)sin(60° +20°)
= sin20° (sin2 60° - sin2 20°)
= sin 20°

[3/4-sin^2 20°]

=

1/4

[3 sin 20° -

sin^3

20°]
=

1/4

sin 3 × 20° =

1/4 √3/2

=

√3/8

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