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PROVE SIN2A+SIN2B-SINC=4COSACOSBSINC PROVE SIN2A+SIN2B-SINC=4COSACOSBSINC
PROVE SIN2A+SIN2B-SINC=4COSACOSBSINC
Dear bayana, he double angle formula:sin 2Θ = 2 sin Θ cos Θsin 2A + sin 2B - sin 2C... = 2 sin A cos A + 2 sin B cos B - 2 sin C cos C Since A + B + C = π ;A is a supplement angle of ( B + C )B is a supplement angle of ( A + C )C is a supplement angle of ( A + B )TAKE NOTE that the sine of supplementary angles are equal !!!sin 2A + sin 2B - sin 2C... = 2 sin A cos A + 2 sin B cos B - 2 sin C cos C ... = 2 sin ( B + C ) cos A + 2 sin ( A + C ) cos B - 2 sin ( A + B ) cos CFrom the Sum of Angle Identity:sin ( α + ß ) = sin α cos ß + cos α sin ßsin 2A + sin 2B - sin 2C... = 2 sin A cos A + 2 sin B cos B - 2 sin C cos C ... = 2 sin ( B + C ) cos A + 2 sin ( A + C ) cos B - 2 sin ( A + B ) cos C... = 2 ( sin B cos C + cos B sin C ) cos A ..... ..... + 2 ( sin A cos C + cos A sin C ) cos B..... ..... – 2 ( sin A cos B + cos A sin B ) cos C... = 2 cos A sin B cos C + 2 cos A cos B sin C..... ..... + 2 sin A cos B cos C + 2 cos A cos B sin C..... ..... – 2 sin A cos B cos C – 2 cos A sin B cos C... = 2 cos A cos B sin C + 2 cos A cos B sin C... = 4 cos A cos B sin C Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple to download the toolbar…. So start the brain storming…. become a leader with Elite Expert League ASKIITIANS Thanks Aman Bansal Askiitian Expert
Dear bayana,
he double angle formula:sin 2Θ = 2 sin Θ cos Θsin 2A + sin 2B - sin 2C... = 2 sin A cos A + 2 sin B cos B - 2 sin C cos C Since A + B + C = π ;A is a supplement angle of ( B + C )B is a supplement angle of ( A + C )C is a supplement angle of ( A + B )TAKE NOTE that the sine of supplementary angles are equal !!!sin 2A + sin 2B - sin 2C... = 2 sin A cos A + 2 sin B cos B - 2 sin C cos C ... = 2 sin ( B + C ) cos A + 2 sin ( A + C ) cos B - 2 sin ( A + B ) cos CFrom the Sum of Angle Identity:sin ( α + ß ) = sin α cos ß + cos α sin ßsin 2A + sin 2B - sin 2C... = 2 sin A cos A + 2 sin B cos B - 2 sin C cos C ... = 2 sin ( B + C ) cos A + 2 sin ( A + C ) cos B - 2 sin ( A + B ) cos C... = 2 ( sin B cos C + cos B sin C ) cos A ..... ..... + 2 ( sin A cos C + cos A sin C ) cos B..... ..... – 2 ( sin A cos B + cos A sin B ) cos C... = 2 cos A sin B cos C + 2 cos A cos B sin C..... ..... + 2 sin A cos B cos C + 2 cos A cos B sin C..... ..... – 2 sin A cos B cos C – 2 cos A sin B cos C... = 2 cos A cos B sin C + 2 cos A cos B sin C... = 4 cos A cos B sin C
Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple to download the toolbar….
So start the brain storming…. become a leader with Elite Expert League ASKIITIANS
Thanks
Aman Bansal
Askiitian Expert
first of all ur question is wrong its sin2a+sin2b-sin2c=4 cosa cosb sinc applying SIN2X=2SINXCOSX A+B+C=180 AND A IS SUPPLEMENT ANGLE OF (B+C) B IS SUPLEMET OF (A+C) AND C OF (A+B) WE GET SIN2A+SIN2B+SIN2C=2SIN(B+C)COSA+2SIN(A+C)COSB-2SIN(A+B)COSC NOW APPLYING SUM PROPERTY SIN(X+Y)=SINX COSY + COSX SINY AND SOLVING WE GET 4COSACOBSINC
first of all ur question is wrong
its sin2a+sin2b-sin2c=4 cosa cosb sinc
applying SIN2X=2SINXCOSX
A+B+C=180
AND A IS SUPPLEMENT ANGLE OF (B+C)
B IS SUPLEMET OF (A+C) AND C OF (A+B)
WE GET
SIN2A+SIN2B+SIN2C=2SIN(B+C)COSA+2SIN(A+C)COSB-2SIN(A+B)COSC
NOW APPLYING SUM PROPERTY
SIN(X+Y)=SINX COSY + COSX SINY
AND SOLVING WE GET 4COSACOBSINC
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