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Question: The value of \(\cos 52{^\circ} + \cos 68{^\circ} + \cos 172{^\circ}\) is...

The value of cos⁡52∘+cos⁡68∘+cos⁡172∘\cos 52{^\circ} + \cos 68{^\circ} + \cos 172{^\circ} is

A

0

B

1

C

2

D

32\frac{3}{2}

Answer

0

Explanation

Solution

cos⁡52∘+cos⁡68∘+cos⁡172∘\cos 52 ^ { \circ } + \cos 68 ^ { \circ } + \cos 172 ^ { \circ }

=(cos⁡52o+cos⁡172o)+cos⁡68o= (\cos{}52^{o} + \cos{}172^{o}) + \cos{}68^{o}

=2cos⁡112ocos⁡60o+cos⁡68o= 2\cos{}112^{o}\cos{}60^{o} + \cos{}68^{o}

=cos⁡112o+cos⁡68o=2cos⁡(90o)cos⁡22o=0= \cos{}112^{o} + \cos{}68^{o} = 2\cos{}(90^{o})\cos{}22^{o} = 0.