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Trignometry

Cool goIITian

Joined:	12 Dec 2009
Post:	42

12 Mar 2010 15:44:54 IST

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prove that :-

None

prove that :- { 1- cosA +cosB - cos(A+B) } / { 1 +cosA - cosB -cos(A+B) } = tan A/2 . cot B/2

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examphobia

Cool goIITian

Joined: 12 Dec 2009

Posts: 42

12 Mar 2010 16:02:35 IST

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plz solve plz....

Dasvidaniya

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Joined: 9 May 2009

Posts: 831

12 Mar 2010 16:17:57 IST

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{ 1- cosA +cosB - cos(A+B) } / { 1 +cosA - cosB -cos(A+B) }

=[ 2 sin^2 (A/2) +2sin A/2 .sin(A/2 +B) ] / [ 2cos^2 (A/2) -2cos A/2 .cos( A/2+B) ]

= { 2sin(A/2) / 2cos(A/2)} [ {sin A/2 + sin( A/2 + B) } / {cos A/2 - cos ( A/2+ B)} ]

= tan A/2 [ 2sin (A+B) /2 . cos(B/2) ] / [ 2sin ( A+B)/2 . sin (B/2) ]

= tan A/2 . cot B/2

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