Question

Cos^2t-2sint*cost+cos^2t

Answer 1

Решение задания смотри на фотографии

Answer 2

To simplify the expression cos^2(t) - 2sin(t)cos(t) + cos^2(t), we can use trigonometric identities and simplification techniques.

Let's start by applying the Pythagorean identity cos^2(t) + sin^2(t) = 1 to the first and third terms:

cos^2(t) - 2sin(t)cos(t) + cos^2(t)
= (1 - sin^2(t)) - 2sin(t)cos(t) + (1 - sin^2(t))

Expanding the expression further:

= 1 - sin^2(t) - 2sin(t)cos(t) + 1 - sin^2(t)
= 2 - 2sin^2(t) - 2sin(t)cos(t)

Next, we can use the double-angle identity for sin(2t) = 2sin(t)cos(t) to simplify further:

= 2 - 2sin^2(t) - sin(2t)

And that is the simplified form of the expression cos^2(t) - 2sin(t)cos(t) + cos^2(t).