NIMCET 2017 Question Paper with solutions

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Question : 89 of 120

Marks: +1, -0

The value of sin 36° is

$√{10+2√5}/4$
$√{10-2√5}/4$
$(√5+1)/4$
$(√5-1)/4$

Solution:

Since, sin 18° =

{√5-1}/4

As we know that, cos 36° = 1 -

sin^2

18°
= 1 - 2

({√5-1}/4)^2

= 1 - 2

({2+1-2√5}/{16})

= 1 -

({6-2√5}/8)

=

{8-62√5}/8)

=

{2+2√5}/8

=

{√5+1}/4

sin^2 36°

+

cos^2

36°
∴

sin^2 36°

= 1 -

cos^2 36°

= 1 -

({√5+1}/2)^2

= 1 -

({5+1+2√5}/{16})

=

{16-62√5}/{16}

=

{10-2√5}/{16}

⇒ sin 36° =

√{{10-2√5}/{16}}

=

√{10-2√5}/4

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