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

  • question_answer
    If \[\sin 2\theta =\cos 3\theta \]and \[\theta \]is an acute angle, then \[\sin \theta \]is equal to [EAMCET 1980]

    A) \[\frac{\sqrt{5}-1}{4}\]

    B) \[\frac{-\sqrt{5}-1}{4}\]

    C) 0

    D) None of these

    Correct Answer: A

    Solution :

    \[\sin 2\theta =\cos 3\theta \]\[\Rightarrow \] \[3\theta =2n\pi \pm \left( \frac{\pi }{2}-2\theta  \right)\] \[\Rightarrow \] \[\theta =\frac{2n\pi }{5}+\frac{\pi }{10}\] or \[\theta =2n\pi -\frac{\pi }{2}\]. Since \[\theta \] is acute Þ \[\theta =\frac{\pi }{10}\] Þ \[\sin \theta =\frac{\sqrt{5}-1}{4}\].


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