To determine which of the given options lie in the span of the set {cos2(x), sin2(x)}, we need to check if each option can be expressed as a linear combination of cos2(x) and sin2(x).

A. tan2(x): This option cannot be expressed as a linear combination of cos2(x) and sin2(x). Therefore, it does not lie in the span of the given set.

B. cos(2x): This option can be expressed as a linear combination of cos2(x) and sin2(x). Using the double angle identity, cos(2x) = cos2(x) - sin2(x). Therefore, it lies in the span of the given set.

C. sin2(2x): This option cannot be expressed as a linear combination of cos2(x) and sin2(x). Therefore, it does not lie in the span of the given set.

D. sin2(x) + 1: This option can be expressed as a linear combination of cos2(x) and sin2(x). sin2(x) + 1 = 1 + sin2(x), which is equivalent to cos2(x). Therefore, it lies in the span of the given set.

In summary, the options that lie in the span of the set {cos2(x), sin2(x)} are B. cos(2x) and D. sin2(x) + 1.

Question

To determine which of the given options lie in the span of the set {cos2(x), sin2(x)}, we need to check if each option can be expressed as a linear combination of cos2(x) and sin2(x).

A. tan2(x): This option cannot be expressed as a linear combination of cos2(x) and sin2(x). Therefore, it does not lie in the span of the given set.

B. cos(2x): This option can be expressed as a linear combination of cos2(x) and sin2(x). Using the double angle identity, cos(2x) = cos2(x) - sin2(x). Therefore, it lies in the span of the given set.

C. sin2(2x): This option cannot be expressed as a linear combination of cos2(x) and sin2(x). Therefore, it does not lie in the span of the given set.

D. sin2(x) + 1: This option can be expressed as a linear combination of cos2(x) and sin2(x). sin2(x) + 1 = 1 + sin2(x), which is equivalent to cos2(x). Therefore, it lies in the span of the given set.

In summary, the options that lie in the span of the set {cos2(x), sin2(x)} are B. cos(2x) and D. sin2(x) + 1.

Knowee AI · Accepted Answer

To determine which of the given options lie in the span of the set {cos2(x), sin2(x)}, we need to check if each option can be expressed as a linear combination of cos2(x) and sin2(x).

A. tan2(x): This option cannot be expressed as a linear combination of cos2(x) and sin2(x). Therefore, it does not lie in the span of the given set.

B. cos(2x): This option can be expressed as a linear combination of cos2(x) and sin2(x). Using the double angle identity, cos(2x) = cos2(x) - sin2(x). Therefore, it lies in the span of the given set.

C. sin2(2x): This option cannot be expressed as a linear combination of cos2(x) and sin2(x). Therefore, it does not lie in the span of the given set.

D. sin2(x) + 1: This option can be expressed as a linear combination of cos2(x) and sin2(x). sin2(x) + 1 = 1 + sin2(x), which is equivalent to cos2(x). Therefore, it lies in the span of the given set.

In summary, the options that lie in the span of the set {cos2(x), sin2(x)} are B. cos(2x) and D. sin2(x) + 1.

Which of the following lie in the span of the set{cos2(x),sin2(x)}? Select all that apply. A. tan2(x) B. cos(2x) C. sin2(2x) D. sin2(x)+1

Question

Which of the following lie in the span of the set {cos2(x), sin2(x)}?

Solution

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