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Trignometry

Blazing goIITian

Joined:	5 Nov 2009
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9 Mar 2010 00:49:58 IST

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Prove the trigonometric identity: cos A (tan A + 2) (2 tan A +1) = 2 secA + 5 sinA

None

Prove the trigonometric identity:cos A (tan A + 2) (2 tan A +1) = 2 secA + 5 sinA

I'm getting just 2sec A.

*curses*

:-S

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NugoRama

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Joined: 11 Mar 2009

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9 Mar 2010 12:13:16 IST

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To Prove: cos A (tan A + 2) (2 tan A +1) = 2 secA + 5 sinA

( tanA + 2 ) ( 2tanA + 1 )

= 2tan^2(A) + 5tanA + 2 ( silly-mistake prone area )

= 2( 1 + tan^2(A) ) + 5 tanA

= 2 sec^2(A) + 5 tanA

= 2 secA / cosA + 5sinA/ cosA

cosA ( tanA + 2 ) ( 2tanA + 1 ) = 2secA + 5sinA

Proved.

The end.

Salonii Sharma

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9 Mar 2010 14:37:03 IST

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Well I could do it later. Without looking at your solution. I just sorta made a silly mistake. Thanks anyway. :-)

edison

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Joined: 19 Oct 2006

Posts: 7537

31 Jan 2011 17:56:52 IST

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Well done NugoRama

rahulmishra

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Joined: 16 Jan 2010

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31 Jan 2011 18:16:17 IST

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LHS = cosA(tanA + 2)(2tanA + 1) = cosA(2tan²A + tanA + 4tanA + 2) = cosA(2tan²A + 5tanA + 2)

= cosA(2sec²A + 5tanA) = 2 secA + 5 sinA = R.H.S Proved

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