Q. 275.0( 1 Vote )

Mark the Correct alternative in the following:

If (2n + 1) x = π, then 2n cos x cos 2x cos22 x ….. cos 2n – 1 x =

A.-1

B. 1

C. 1/2

D. None of these

Answer :

Given (2n – 1) x = π


Then evaluate the expression


2n cos x cos 2x cos22 x ….. cos 2n – 1 x


by taking a 2 from 2n and multiplying and dividing by sin x, we get



[by using the formula sin 2x = 2 sin x cos x]



Now borrowing another 2 from 2n-1




These iterations repeat till we reach the last term





As already given that


2n x + x = 180°


2n x = 180° - x


So substituting the same in the above solution



So the answer is option B.

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