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

  • question_answer
    \[\frac{\sec 8A-1}{\sec 4A-1}=\] [MP PET 1995]

    A) \[\frac{\tan 2A}{\tan 8A}\]

    B) \[\frac{\tan 8A}{\tan 2A}\]

    C) \[\frac{\cot 8A}{\cot 2A}\]

    D) None of these

    Correct Answer: B

    Solution :

    \[\frac{\sec 8A-1}{\sec 4A-1}=\frac{1-\cos 8A}{\cos 8A}.\frac{\cos 4A}{1-\cos 4A}\] \[=\frac{2{{\sin }^{2}}4A}{\cos 8A}\frac{\cos 4A}{2{{\sin }^{2}}2A}\]\[=\frac{2\sin 4A\cos 4A}{\cos 8A}\frac{\sin 4A}{2{{\sin }^{2}}2A}\] \[=\tan 8A\frac{2\sin 2A\cos 2A}{2{{\sin }^{2}}2A}=\frac{\tan 8A}{\tan 2A}.\]

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