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Trignometry

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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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hemang

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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. :-)

Arjun Virmani

Forum Expert

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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