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

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

A

`1//4`

B

4

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
Consider `sqrt(3)" cosec" 20^(@)-sec20^(@)`
`=(sqrt(3))/(sin20^(@))-(1)/(cos20^(@))=(sqrt(3)cos20^(@)-sin20^(@))/(sin20^(@)cos20^(@))`
Multiply and divide by 4
`=(4)/(2sin20^(@)cos20^(@))(sqrt(3)/(2)cos20^(@)-(1)/(2)sin20^(@))`
`(becausesin2theta=2sinthetacostheta)`
`=(4)/(sin40^(@))(sin60^(@)cos20^(@)-cos60^(@)sin20^(@))`
`=(4)/(sin40^(@))sin(60^(@)-20^(@))`
`(becausesin(A-B)=sinAcosB-cosAsinB)`
=4
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