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Question
`sqrt(3) "cosec" 20^circ - sec 20^circ` is equal to ______.
Options
2
2 sin 20° cosec 40°
4
4 sin 20° cosec 40°
MCQ
Fill in the Blanks
Solution
`sqrt(3) "cosec" 20^circ - sec 20^circ` is equal to 4.
Explanation:
`sqrt(3) "cosec" 20^circ - sec 20^circ`
= `(tan 60^circ)/(sin 20^circ) - 1/(cos 20^circ)`
= `(sin 60^circ cos 20^circ - sin 20^circ cos 60^circ)/(cos 60^circ sin 20^circ cos 20^circ)`
= `(sin 40^circ)/(cos 60^circ sin 20^circ cos 20^circ)`
= `(2 sin 20^circ cos 20^circ)/(1/2 (sin 20^circ cos 20^circ))`
= 4
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Trigonometric Functions of Triple Angle
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