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Trignometry

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 Joined: 8 Aug 2011 Post: 1
8 Aug 2011 21:55:54 IST
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Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

sec4a(1 - sin4a) - 2tan2a= 1

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Joined: 27 Dec 2010
Posts: 1508
9 Aug 2011 09:46:24 IST
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sec4a(1 - sin4a) = sec4a - tan4a. ....(1)

also sec4a = (1 + tan2a)2 so putting thsi value in (1) we get,

1 + tan4a + 2tan2a - tan4a = 1 + 2tan2a

and that is what we have tp prove. :-)

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Joined: 1 Jun 2009
Posts: 1330
26 Jul 2012 17:00:50 IST
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Taking L.H.S.

=sec4a . (1 - sin4a)             - 2tan2a

Using a2 - b2= (a+b)(a-b)

=sec4a (1-sin2a) (1+sin2a)  - 2tan2a

=sec4a cos2a  (1+sin2a)       -2tan2a

=sec2a  (1+sin2a)       -2tan2a

= sec2a + tan2a -2tan2a

=sec2a - tan2a = 1    [Identity]      = R.H.S. [Hence Proved]

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