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Trignometry

Hot goIITian

 Joined: 4 Jun 2012 Post: 138
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.

Blazing goIITian

Joined: 8 Oct 2008
Posts: 8064
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

New kid on the Block

Joined: 25 Jul 2012
Posts: 4
25 Jul 2012 12:13:06 IST
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wrong

Hot goIITian

Joined: 4 Jun 2012
Posts: 138
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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