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If N = 1 , 2 , 3 , . . . , Then Cos α Cos 2 α Cos 4 α . . . Cos 2 N − 1 α is Equal to

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Question

If \[n = 1, 2, 3, . . . , \text{ then }  \cos \alpha \cos 2 \alpha \cos 4 \alpha . . . \cos 2^{n - 1} \alpha\] is equal to

 

Options

  • \[\frac{\sin 2n \alpha}{2n \sin \alpha}\]

  • \[\frac{\sin 2^n \alpha}{2^n \sin 2^{n - 1} \alpha}\]

     

  • \[\frac{\sin 4^{n - 1} \alpha}{4^{n - 1} \sin \alpha}\]

  • \[\frac{\sin 2^n \alpha}{2^n \sin \alpha}\]

     

MCQ
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Solution

\[\frac{\sin 2^n \alpha}{2^n \sin \alpha}\] \[\because \cos \alpha \cos 2 \alpha \cos 4\alpha . . . \cos 2^{n - 1} \alpha = \frac{\sin 2^n \alpha}{2^n \sin \alpha}\]
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Values of Trigonometric Functions at Multiples and Submultiples of an Angle
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Chapter 9: Values of Trigonometric function at multiples and submultiples of an angle - Exercise 9.5 [Page 45]

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R.D. Sharma Mathematics [English] Class 11
Chapter 9 Values of Trigonometric function at multiples and submultiples of an angle
Exercise 9.5 | Q 35 | Page 45

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