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Find the value of 3 cosec 20° – sec 20° - Mathematics

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प्रश्न

Find the value of `sqrt(3)` cosec 20° – sec 20°

योग

उत्तर

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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अध्याय 3: Trigonometric Functions - Solved Examples [पृष्ठ ४०]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 11
अध्याय 3 Trigonometric Functions
Solved Examples | Q 3 | पृष्ठ ४०

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