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Question

The value of cos200+cos2300+cos2450+cos2600+cos2900 is

A
12
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B
32
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C
52
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D
72
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Solution

The correct option is B 52
Consider the following identity
cos2α+cos2(900α)
=cos2α+sin2α
=1

Applying this identity in the above expression
cos20+cos2300+cos2450+cos2600+cos2900
=cos20+cos2900+cos2300+cos2600+cos2450
=cos20+cos2(90000)+cos2300+cos2(900300)+12
=1+1+12 ...(from the identity)
=52

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