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

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

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Solution: We have ,

\ Rightarrow 3sinA+4cosB=6 ........(1)\ \Rightarrow 4cosB+3cosA=1 ........(2)

Squaring and adding (1) and (2)  we get

\ 9+16+24 imes sin(A+B)=37\ \Rightarrow 24sin(A+B)=12\ \Rightarrow sin(A+B)=1/2\ \ sin(pi -C)=1/2\ \ Rightarrow C=pi /6

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Deependra Verma

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