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10th Class Mathematics Quadratic Equations Question Bank Quadratic Equation

  • question_answer
    tan A, tan B are roots of\[3{{x}^{2}}-5x+6=0\]. then \[si{{n}^{2}}\left( A+B \right)\]

    A)  \[\frac{14}{15}\]                                  

    B)  \[\frac{25}{34}\]

    C)  \[\frac{13}{25}\]                                  

    D)  \[\frac{11}{46}\]

    Correct Answer: B

    Solution :

    (b): \[\tan A+\operatorname{tanB}=\frac{5}{3}\]and\[\tan A\operatorname{tanB}=2\] \[\tan (A+B)=W=\frac{-5}{3}\] \[\therefore {{\sin }^{2}}(A+B)=\frac{1}{\cos e{{c}^{2}}A}=\frac{1}{1+{{\cot }^{2}}B}\] \[=\frac{1}{1+\frac{9}{25}}=\frac{25}{34}\]


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