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

  • question_answer
    The value of \[\tan 7\frac{1}{2}{}^\circ \] is equal to [J & K 2005]

    A) \[\sqrt{6}+\sqrt{3}+\sqrt{2}-2\]

    B) \[\sqrt{6}-\sqrt{3}+\sqrt{2}-2\]

    C) \[\sqrt{6}-\sqrt{3}+\sqrt{2}+2\]

    D) \[\sqrt{6}-\sqrt{3}-\sqrt{2}-2\]

    Correct Answer: B

    Solution :

    We have \[\tan A=\frac{\sin A}{\cos A}=\frac{2\sin A\cos A}{2{{\cos }^{2}}A}=\frac{\sin 2A}{1+{{\cos }^{2}}A}\] Putting \[A=7{{\frac{1}{2}}^{o}}\Rightarrow \tan 7{{\frac{1}{2}}^{o}}=\frac{\sin {{15}^{o}}}{1+\cos {{15}^{o}}}\] On simplification, we get\[\tan 7{{\frac{1}{2}}^{o}}=\sqrt{6}-\sqrt{3}+\sqrt{2}-2\].

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