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The value of cos(-89^(@))+cos(-87^(@))+c...

The value of `cos(-89^(@))+cos(-87^(@))+cos(-85^(@))+…+cos(85^(@))+cos(87^(@))+cos(89^(@))` is equal to

A

`cosec 1^(@)`

B

`sec 1^(@)`

C

`2 sec 1^(@)`

D

`2 cosec 1^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
`cos(-89^(@))+cos(-87^(@))+cos(-85^(@))+…+cos(85^(@))+cos(87^(@))+cos(89^(@))`
`=2(cos1^(@)+cos 3^(@)+cos5^(@)+…+cos 89^(@))`
`=2.(sin(45^(@)))/(sin(1^(@))){cos((1^(@)+89^(@))/(2))}`
`=(2sin 45^(@)cos 45^(@))/(sin1^(@))`
`=(sin 90^(@))/(sin 1^(@))`
`cosec 1^(@)`
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