Maharashtra State BoardHSC Science (General) 11th
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Prove the following: 3 cosec20∘-sec20∘ = 4 - Mathematics and Statistics

Sum

Prove the following:

`sqrt(3)  "cosec"20^circ - sec20^circ` = 4

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Solution

L.H.S. = `sqrt(3)  "cosec"20^circ - sec20^circ`

= `sqrt(3)/sin20^circ  - 1/cos20^circ`

= `2((sqrt(3)/2)/sin20^circ  - (1/2)/cos20^circ)`

= `2(sin60^circ/sin20^circ  - cos60^circ/cos20^circ)`

= `2((sin60^circ cos20^circ -  cos60^circ sin20^circ)/sin20^circ cos20^circ)`

= `(2sin(60^circ - 20^circ))/(1/2(2sin20^circ cos20^circ))`

= `(4sin40^circ)/(sin40^circ)`

= 4

= R.H.S.

Concept: Trigonometric Functions of Triple Angle
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 3 Trigonometry - 2
Miscellaneous Exercise 3 | Q II. (30) | Page 58
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