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Question
Find the value of `sqrt(3)` cosec 20° – sec 20°
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Solution
We have
`sqrt(3)` cosec 20° – sec 20° = `sqrt(3)/(sin20^circ) - 1/(cos20^circ)`
= `(sqrt(3) cos 20^circ - sin 20^circ)/(sin 20^circ cos 20^circ)`
= `4((sqrt(3)/2 cos 20^circ - 1/2 sin 20^circ)/(2sin 20^circ cos 20^circ))`
= `4((sin60^circ cos20^circ - cos60^circ sin20^circ)/sin40^circ)`
= `4((sin(60^circ - 20^circ))/(sin 40^circ))`
= 4
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