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if Cos A=Cos B Cos Cand A+B+C=pi then cot B Cot C will equel to??

if Cos A=Cos B Cos Cand A+B+C=pi
then cot B Cot C will equel to??

Grade:12th pass

3 Answers

Amit
405 Points
3 years ago
We know A+B+C=π. Hence A=π-(B+C).Putting it in CosA=CosB.CosC we get Cos(π-(B+C))=cosB.cosC. Using formula of cos(π-x)=-Cosx, we get Cos(B+C)=-cosB.cosC.Expanding cos(B+C) equal to cosB.CosC-sinB.sinC and taking cosB.CosC term other side we get 2CosB.CosC=sinB.sinC.Hence cotB.cotC=1/2
Soumendu Majumdar
159 Points
3 years ago
Dear Student,
A + B + C = 180 degrees
implies A = 180 – ( B + C )
cos A = cos B cos C
implies    cos (180 – B – C) = cos B cos C
implies    – cos ( B + C ) = cos B cos C
implies    – cos B cos C + sin B sin C = cos B cos C
implies     2 cos B cos C = sin B sin C
Hence      cot B cot C = ½
 
Hope it helps!
Kushagra Madhukar
askIITians Faculty 629 Points
one year ago
Dear student,
Please find the solution to your problem.
 
A + B + C = 180 degrees
implies A = 180 – ( B + C )
cos A = cos B cos C
implies    cos (180 – B – C) = cos B cos C
implies    – cos ( B + C ) = cos B cos C
implies    – cos B cos C + sin B sin C = cos B cos C
implies     2 cos B cos C = sin B sin C
Hence      cot B cot C = ½
 
Thanks and regards,
Kushagra

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