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

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

A

`4`

B

`3`

C

`2`

D

`1`

Text Solution

Verified by Experts

The correct Answer is:
A
Consider `sqrt(3)" cosec"20^(@)-sec20^(@)=(sqrt(3))/(sin20^(@))-(1)/(cos20^(@))`
`=(sqrt3cos20^(@)-sin20^(@))/(sin20^(@)cos20^(@))`
Multiply and divide by 2 in `N^(r )`.
`=2((sqrt(3)/(2)cos20^(@)-(1)/(2)sin20^(@))/(sin20^(@)cos20^(@)))`
`=2((sin60^(@)cos20^(@)-cos60^(@)sin20^(@))/(sin20^(@)cos20^(@)))`
`(becausesin60^(@)=(sqrt(3))/(2)andcos60^(@)=(1)/(2))`
`=(2xx2[sin(60^(@)-20^(@))])/(2sin20^(@)cos20^(@))`
`(becausesinAcosB-cosAsinB=sin(A-B)and sin2theta=2sinthetacostheta)`
`=(4sin40^(@))/(sin40^(@))=4`
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