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sqrt(3)cossec2 0^0-sec2 0^0...

`sqrt(3)cossec2 0^0-sec2 0^0`

A

4

B

2

C

1

D

`-4`

Text Solution

Verified by Experts

The correct Answer is:
A
`(sqrt(3)cos20^(@)-sin20^(@))/(sin20^(@)cos20^(@))`
`=(sqrt(3)cos20^(@)-sin20^(@))/(sin20^(@)cos20^(@))`
`=(2((sqrt(3))/(2)cos20^(@)-(1)/(2)sin20^(@)))/(sin20^(@)cos20)`
`=(2(cos30^(@)cos20^(@)-sin30^(@)sin20^(@)))/(((2sin20^(@)cos20^(@))/(2)))`
`=(4[cos(30^(@)+20^(@))])/(sin40^(@))`
`=(4cos50^(@))/(sin40^(@))=(4"cos"(90^(@)-40^(@)))/(sin40^(@))=(4sin40^(@))/(sin40^(@))=4`.
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