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

  • question_answer
    If \[\sin \alpha =\frac{336}{625}\]and \[450{}^\circ <\alpha <540{}^\circ ,\] then \[\sin \left( \frac{\alpha }{4} \right)=\]

    A) \[\frac{1}{5\sqrt{2}}\]

    B) \[\frac{7}{25}\]

    C) \[\frac{4}{5}\]

    D) \[\frac{3}{5}\]

    Correct Answer: C

    Solution :

    \[\sin \alpha =\frac{336}{625}\] Þ \[\cos \alpha =-\sqrt{1-{{\sin }^{2}}\alpha }=-\sqrt{1-{{\left( \frac{336}{625} \right)}^{2}}}\],                [\[\because \]\[\alpha \]is in II Quadrant] Now, \[\cos \left( \frac{\alpha }{2} \right)=-\sqrt{\frac{1+\cos \alpha }{2}}=-\frac{7}{25}\], [\[\because \frac{\alpha }{2}\]is in III Quadrant] \[\therefore \,\,\,\sin \left( \frac{\alpha }{4} \right)=+\sqrt{\frac{1-\cos (\alpha /2)}{2}}=\sqrt{\frac{1+\frac{7}{25}}{2}}=\frac{4}{5}\], [\[\because \,\frac{\alpha }{4}\]is in II Quadrant]

You need to login to perform this action.
You will be redirected in 3 sec spinner