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The value of 2(cos^(2)20^(@)+cos^(2)140^...

The value of `2(cos^(2)20^(@)+cos^(2)140^(@)+cos^(2)100^(@))` is

A

`3//2`

B

3

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`2(cos^(2)20^(@)+cos^(2)140^(@)+cos^(2)100^(@))`
`=3+cos 40^(@)+cos 280^(@)+cos 200^(@)`
`=3+2cos 120^(@) cos 160^(@) + cos 200^(@)`
`= 3-cos 160^(@)+cos 200^(@)`
`=3-cos(360^(@)-200^(@))+cos 200^(@)`
`=3-cos 200^(@)+cos 200^(@)`
= 3
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