Question

Express the derivative of sin2x in terms of cos2x using cos2x=cos^(2)x-sin^(2)x.

Answer 1

The derivative of sin^2(x) in terms of cos^2(x) can be expressed as 2sin(x) * (cos^2(x) - sin^2(x)).

Step-by-step explanation:

To express the derivative of sin^2(x) in terms of cos^2(x), we can use the trigonometric identity cos^2(x) = cos^2(x) - sin^2(x). Let's differentiate sin^2(x) with respect to x using the chain rule:

d/dx sin^2(x) = 2sin(x) * cos(x)

Now, we can substitute cos^2(x) = cos^2(x) - sin^2(x) to get the derivative of sin^2(x) in terms of cos^2(x):

d/dx sin^2(x) = 2sin(x) * (cos^2(x) - sin^2(x))