Prove that Cos(b-c)+Cos(c-a)+Cos(a-b)=-3/2 if Cosa+Cosb+Cosc=0 and Sina+Sinb+Sinc=0

Dear vinay,

squaring the equations 

Cosa+Cosb+Cosc=0    and  

 we get 

      cos² a + cos² b+ cos² c + 2cosacosb+2cosbcosc+2cosacosc = 0

and similarly sin² a +sin²  b +sin²  c+ 2 sinasinb+2 sinasinb+2 sinasinb=0

adding the above two equations we get 

3 + 2(sinasinb+cosacosb+sinasinb+cosacosb+sinasinb+cosacosb)=0

and by formula sinasinb + cosacosb = cos(a-b) and replacing

we get   

We are all IITians and here to help you in your IIT JEE preparation.

Now you can win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar: Click here to download the toolbar.. 

jitender

askiitians expert