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

  • question_answer
    If \[3({{\sec }^{2}}\theta +{{\tan }^{2}}\theta )=5\], then the general value of \[\theta \] is

    A)   \[2n\pi +\frac{\pi }{6}\]

    B) \[2n\pi \pm \frac{\pi }{6}\]

    C) \[n\pi \pm \frac{\pi }{6}\]

    D) \[n\pi \pm \frac{\pi }{3}\]

    Correct Answer: C

    Solution :

    \[{{\sec }^{2}}\theta +{{\tan }^{2}}\theta =\frac{5}{3}\], also\[{{\sec }^{2}}\theta -{{\tan }^{2}}\theta =1\] \[\Rightarrow \] \[{{\tan }^{2}}\theta =\frac{1}{3}={{\tan }^{2}}\left( \frac{\pi }{6} \right)\Rightarrow \theta =n\pi \pm \frac{\pi }{6}\].


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