JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Trigonometrical ratios of multiple and sub multiple angles

  • question_answer
    If \[\alpha \] is a root of \[25{{\cos }^{2}}\theta +5\cos \theta -12=0\], \[\pi /2<\alpha <\pi \], then \[\sin 2\alpha \]is equal to [UPSEAT 2001]

    A) \[24/25\]

    B) \[-24/25\]

    C) \[13/18\]

    D) \[-13/18\]

    Correct Answer: B

    Solution :

      Since a is a root of  \[25{{\cos }^{2}}\theta +5\cos \theta -12=0\] \\[25{{\cos }^{2}}\alpha +5\cos \alpha -12=0\] Þ \[\cos \alpha =\frac{-5\pm \sqrt{25+1200}}{50}\] \[=\frac{-5\pm 35}{50}\] Þ \[\cos \alpha =-4/5\] \[[\because \pi /2<\alpha <\pi \Rightarrow \cos \alpha <0]\] \[\therefore \]\[\sin 2\alpha =2\sin \alpha \cos \alpha =-24/25\].

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