Question

The range of 16 Sinx Cosx cos2x Cos4x Cos8x is ..
1 1
3 3
1) (-1, 1]
2)
3)
2'2
4) -13,2
4 4
With Explation​

Answer 1

Given: The expression 16sinx cosx cos2x cos4x cos8x

To find: The range of the given expression.

Solution:

• Now we have given the expression as:

                16sinx cosx cos2x cos4x cos8x

• Now we can rewrite it as:

                8 x 2sinx cosx cos2x cos4x cos8x

• Now we know the identity as: 2sinx cosx = sin2x .............(i)

• So applying it, we get:

                8 sin2x cos2x cos4x cos8x

• Again we can rewrite it as:

                4 x 2sin2x cos2x cos4x cos8x

• Applying (i) again, we get:

                4 x sin4x cos4x cos8x

• Again we can rewrite it as:

                2 x 2sin4x cos4x cos8x

•  Applying (i) again, we get:

                2 sin8x cos8x

•  Applying (i) again, we get:

                sin16x

• So the range of sin16x  is [-1,1]

Answer:

             So the range of 16sinx cosx cos2x cos4x cos8x  is [-1,1].