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In a triangle ABC , if 3 sin A +4 cos B=6 ; and 4 sin B +3 cos A =1 , then a possible value of angle C is

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Solution:   We have ,

                   3sin A +4 cos B =6       .......(1)

                   4 sin B +3 cos A=1        ........(2)

              Squaring and adding the  two equations , we have

             9+16+24+sin (A+B)=37

    Rightarrow        sin (A+B)=frac12Rightarrow sin (pi -C)=frac12

  Rightarrow                    C=fracpi6.

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Deependra Verma

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