Solve qn no 13: 13 If A+B+C = , then find the value of - Maths - Determinants

Question

Solve qn no 13:

13

If   A + B + C   = π ,   then   find  
the   value   of          
              sin   A + B +
C   sin   B cost   C - sin   A 0 tan   A
cos   A + B - tan   A 0 Using   propertles   of
  determinant ,   prove   that      
                 
        b + c a - b a c + a b - c b a + b c - a
c = 3 abc - a 3 - b 3 - c 3

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

A+B+C=π⇒A+C=π-B,A+B=π-C and B+C=π-AThus
the determinant
becomessinπsinπ-BcosC-sinB0tanAcos(π-C)tanπ-A0sinπ=0,sinπ-B=sinB,cosπ-C=-cosC,tanπ-A=-tanAIt
is a skew symmetric matrix of the order 3 Thus, by property of
determinats , we
get△=0⇒0sinBcosC-sinB0tanA-cosC-tanA0=0

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Solve qn no 13: 13. If A + B + C = π , then find the value of sin A + B + C sin B cost C - sin A 0 tan A cos A + B - tan A 0 Using propertles of determinant , prove that b + c a - b a c + a b - c b a + b c - a c = 3 abc - a 3 - b 3 - c 3