Maths-
General
Easy

Question

16 sin x cos space x cos space 2 x cos space 4 x cos space 8 x element of

  1. [-1,1]
  2. [negative 1 fourth comma 1 fourth]
  3. [negative 3 over 4 comma 3 over 4]
  4. [negative fraction numerator square root of 3 over denominator 2 end fraction comma fraction numerator square root of 3 over denominator 2 end fraction]

hintHint:

In this question, we have to find the range of 8 sin x.cos x.cos 2x.cos 4x.cos 8x. For that first we will simplify the trigonometric function and later as we know range of sin y and cos y is [-1,1], so, using this we can find the range of the given function.

The correct answer is: [-1,1]


    f(x) = 8 sin x.co x.cos 2x.cos 4x.cos 8x
    =4sin 2x.cos 4x.cos 8x
    =2sin 8x.cos 8x
    =sin 16x
    A s comma space minus 1 less or equal than sin space y less or equal than 1
rightwards double arrow negative 1 less or equal than sin space 16 x less or equal than 1
    So, range is [-1, 1].

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