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Trignometry

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11 Apr 2010 11:58:38 IST

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find value of sin 36 , cos 18?

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find value of sin 36 , cos 18?

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Himaya Iyer

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11 Apr 2010 16:14:25 IST

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let 18=A...5A=90....2A+3A=90..2A=90-3A...sin(2A)=sin(90-3A)..sin(2A)=cos(3A)..put values of sin (2A) and cos(3A)get a quadratic and solve it..

rahulmishra

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16 Apr 2010 19:35:43 IST

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Let A = 18⁰
=> 5A = 90⁰
=> 3A + 2 A = 90⁰
=> 3A = 90² - 2A
=> Sin 3A = Cos 2A
=> 3 Sin A - 4 Sin³ A = 1 - 2 Sin² A
=> 3 Sin A - 4 Sin³ A - 1 + 2 Sin² A = 0
=> 4 Sin³A - 2 Sin² A - 3 Sin A + 1 = 0
putting sin A = x we have,
4 x³ - 2 x² - 3x + 1 = 0
=> 4x³ - 4 x² + 2 x² - 2x - x + 1 = 0
=> 4 x²(x - 1) + 2x (x - 1) - 1 (x - 1) = 0
=> (x - 1) (4x² + 2x - 1) = 0
either, x = 1 or 4x² + 2x - 1 = 0
But, since Sin 18⁰ cannot be equal to 1 so,
4x² + 2x - 1 = 0
Solve this quadratic eqn. and you will get the value of sin 18⁰ i.e., root (5) - 1 / 4
Then find cos x
Then Sin 36⁰ = 2 sin 18<sup>0</sup> . cos 18<sup>0</sup>

ajay

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22 Aug 2012 13:27:05 IST

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find value of sin 36 , cos 18

ajay

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Joined: 22 Aug 2012

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22 Aug 2012 13:30:21 IST

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what is the minimum value of [x] (a) -1 (b) 0 (c) 1 (d)2

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