11th Class Mathematics Trigonometric Identities Question Bank Critical Thinking

  • question_answer If A lies in the third quadrant and \[3\,\tan A-4=0,\] then \[5\,\sin 2A+3\,\sin A+4\,\cos A=\] [EAMCET 1994]

    A) 0

    B) \[\frac{-24}{5}\]

    C) \[\frac{24}{5}\]

    D) \[\frac{48}{5}\]

    Correct Answer: A

    Solution :

    \[3\tan A-4=0\Rightarrow \tan A=\frac{4}{3}\Rightarrow \sin A=-\frac{4}{5},\cos A=-\frac{3}{5}\] \[\therefore \] \[5\sin 2A+3\sin A+4\cos A\] = \[10\sin A\cos A+3\sin A+4\cos A\] = \[10\,\left( \frac{12}{25} \right)-\frac{12}{5}-\frac{12}{5}=0\].

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