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Trignometry

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13 Jul 2012 11:44:00 IST

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trigonometry

Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

if sum of four angles be 180 degrees, prove that the sum of the product of their cosine taken two together is equal to the sum of the products of their sines taken similarly.

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Sagar Saxena

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20 Jul 2012 19:00:15 IST

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let a,b,c,d are the four angle.then a+b+c+d=180

now we have to prove sinasinb+sinbsinc+sincsind+sindsina=cosacosb+cosbcosc+cosccosd+cosdcosa

r.h.s.=cos(a+b)+cos(a-b)+cos(b+c)+cos(b-c)+cos(c+d)+cos(c-d)+cos(d+a)+cos(d-a)/2............{cosacosb=cos(a+b)+cos(a-b)/2

now putting a+b=180-(c+d) and b+c=180-(a+d) and solving we get

cos(a-b)+cos(b-c)+cos(c-d)+cos(d-a)/2

on expanding we get l.h.s.,hence proved

sen mu7 uryn

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25 Jul 2012 12:13:06 IST

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wrong

harshika rai

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25 Jul 2012 14:15:55 IST

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sen mu7 uryn you are wrong.The solution is correct only.What's wrong in it?

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