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Prove that: sqrt(3)"cosec"20^(@)-sec20...

Prove that:
`sqrt(3)"cosec"20^(@)-sec20^(@)=4`

Text Solution

Verified by Experts

LHS `=(sqrt(3))/(sin20^(@))-(1)/(cos 20^(@))=(sqrt(3)cos20^(@)-sin20^(@))/(sin20^(@),cos20^(@))`
`=(4((sqrt(3))/(2)cos20^(@)-(1)/(2)sin20^(@)))/(2 sin 20^(@)cos 20^(@))=(4(sin60.cos20^(@)-cos60^(@).sin20^(@)))/(sin40^(@))`
`=4.(sin(60^(@)-20^(@)))/(sin40^(@))=4.(sin40^(@))/(sin40^(@))=4=`RHS.
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