Question

Use the squared identities to simplify 2cos²(x) cos²(x).

a) 2cos⁴(x)
b) 4cos⁴(x)
c) 2cos⁸(x)
d) 4cos⁸(x)

Answer 1

The expression 2cos²(x) cos²(x) simplifies to 2cos´(x) by multiplying the cosines to the fourth power and then multiplying by 2, which corresponds to option a) 2cos´(x).

Step-by-step explanation:

To simplify the expression 2cos²(x) cos²(x), we can recognize that it's equivalent to 2 multiplied by cos²(x) times cos²(x). This simplifies further by multiplying the cosines together first, yielding cos´(x), and then multiplying it by 2:

2(cos²(x) × cos²(x)) = 2cos´(x)

Since the cosines are being multiplied together, we raise the cosine to the fourth power and then multiply by 2:

2cos´(x) is the simplified form of the original expression, which corresponds to option a) 2cos´(x).