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Question

Mathematics Question on Differential equations

The value of 2 sin(12°) – sin(72°) is

A

5(1−3)4\frac{\sqrt5(1-\sqrt3)}{4}

B

1−58\frac{1-\sqrt5}{8}

C

3(1−5)2\frac{\sqrt3(1-\sqrt5)}{2}

D

3(1−5)4\frac{\sqrt3(1-\sqrt5)}{4}

Answer

5(1−3)4\frac{\sqrt5(1-\sqrt3)}{4}

Explanation

Solution

The correct option is:(D): 3(1−5)4\frac{\sqrt3(1-\sqrt5)}{4}.

2sin12o-sin12o

=sin12o-cos42o

=sin12o-sin48o

=2sin18o.cos30o

=−2(5−14).32=-2(\frac{\sqrt5-1}{4}).\frac{\sqrt3}{2}

3(1−5)4\frac{\sqrt3(1-\sqrt5)}{4}