JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Solution of trigonometrical equations

  • question_answer
    If \[\sin \theta =\sqrt{3}\cos \theta ,-\pi <\theta <0\], then \[\theta =\] [MP PET 1992]

    A) \[-\frac{5\pi }{6}\]

    B) \[-\frac{4\pi }{6}\]\[\]

    C) \[\frac{4\pi }{6}\]

    D) \[\frac{5\pi }{6}\]

    Correct Answer: B

    Solution :

    \[\tan \theta =\sqrt{3}=\tan \frac{\pi }{3}\Rightarrow \theta =n\pi +\frac{\pi }{3}\] For \[-\pi <\theta <0\] \[\text{Put}\,\,n=-1\], we get\[\theta =-\pi +\frac{\pi }{3}=\frac{-2\pi }{3}\text{or }\frac{-4\pi }{6}\].


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