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Show that sqrt(3)cosec 20^@ - sec 20^@= ...

Show that `sqrt(3)cosec 20^@ - sec 20^@= 4`

Text Solution

Verified by Experts

`sqrt3 cosec 90^@ - sec 20^@ = 4`
LHS
`sqrt3 cosec 90^@ - sec 20^@`
`= sqrt3 1/(sin 20^@) -1/(cos 20^@) = ( sqrt3 cos 90^@ - sin 20^@)/(sin20^@* cos20^@)`
`= (sqrt3 cos 20^@ - sin 20^@)/(sin 20^@ * cos 20^@)`
`= (sqrt3/2cos 20^@ - 1/2 sin 20^@)/(1/2 sin 20^@ cos20^@)`
`= (sin 60^@cos20^@ - cos 60^@sin20^@)/(1/2 sin 20^@cos20^@)`
`= 2 xx 2 xx (sin (60^@-20^@))/(2 sin20^@cos90^@)`
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