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10th Class Mathematics Introduction to Trigonometry Question Bank Introduction to Trigonometry

  • question_answer
    If \[\sin A:\cos A=4:7,\] then the value of \[\frac{7\sin A-3\cos A}{7\sin A+2\cos A}\] is __________.

    A) \[\frac{3}{14}\]                                  

    B) \[\frac{3}{2}\]

    C)  \[\frac{1}{3}\]                       

    D)         \[\frac{1}{6}\]           

    Correct Answer: D

    Solution :

    \[\frac{\sin A}{\cos A}=\frac{4}{7}\]                        (Given) Now,     \[\frac{7\sin A-3\cos A}{7\sin A+2\cos A}\] Dividing numerator and denominator by \[\cos A,\] we get \[\frac{\frac{7\sin A}{\cos A}-3}{\frac{7\sin A}{\cos A}+2}=\frac{7\times \frac{4}{7}-3}{7\times \frac{4}{7}+2}=\frac{1}{6}\]


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