Question

1) cos2t * 2 * 2t = ? 2) p/2 * ln4p= ? p - это число пиНадо просто упростить

Answer 1

Cos2t*2*2t=cos2t*4t=4t*cos2t

Answer 2

1. To simplify the expression cos(2t) * 2 * 2t, we can start by using the double angle identity for cosine: cos(2t) = 2cos^2(t) - 1.

Substituting this into the expression, we have:

(2cos^2(t) - 1) * 2 * 2t

Expanding the expression further, we get:

4cos^2(t) * 2 * 2t - 2 * 2t

Simplifying the expression, we have:

16cos^2(t)t - 4t

Therefore, cos(2t) * 2 * 2t simplifies to 16cos^2(t)t - 4t.

2. To simplify the expression (p/2) * ln(4p), we can use the properties of logarithms and simplify it further.

Using the logarithmic property log(a*b) = log(a) + log(b), we have:

(p/2) * ln(4) + (p/2) * ln(p)

Now, we can simplify the expression by multiplying the terms:

(p/2) * (ln(4) + ln(p))

Next, we can simplify ln(4) using the natural logarithm of a constant:

ln(4) = ln(2^2) = 2 * ln(2)

Substituting this back into the expression, we have:

(p/2) * (2 * ln(2) + ln(p))

Finally, we can simplify it further by combining the terms:

(p/2) * (2ln(2) + ln(p)) = p(ln(2) + ln(p))/2

Therefore, (p/2) * ln(4p) simplifies to p(ln(2) + ln(p))/2.