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The value of 2 cos10^(@)+sin 100^(@)+sin...

The value of `2 cos10^(@)+sin 100^(@)+sin 1000^(@)+sin 10000^(@)` is

A

0

B

`sin 10^(@)`

C

`cos 10^(@)`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
C
`2cos 10^(@)+sin 100^(@)+sin 1000^(@)+sin 10000^(@)`
`=2cos 10^(@)+sin(90^(@)+10^(@))+sin(3xx60^(@)-80^(@))+sin(28xx360^(@)-80^(@))`
`=2cos10^(@)+cos10^(@)-sin80^(@)-sin80^(@)`
`=3 cos10^(@)-2cos 10^(@)`
`=cos 10^(@)`
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