Question

Cos2x=1/4; sin^2x=?;

Answer 1

Ответ: 3/8__________________________

Answer 2

To find the value of sin^2(x), we can start by using the Pythagorean identity for sine and cosine:

sin^2(x) + cos^2(x) = 1

We already have the value of cos(2x) as 1/4. Now, we can use the double angle identity for cosine:

cos(2x) = 2cos^2(x) - 1

Substitute the given value of cos(2x):

1/4 = 2cos^2(x) - 1

Add 1 to both sides:

5/4 = 2cos^2(x)

Now, divide both sides by 2:

cos^2(x) = 5/8

Now, to find sin^2(x), we can use the Pythagorean identity:

sin^2(x) + cos^2(x) = 1

Substitute the value of cos^2(x):

sin^2(x) + 5/8 = 1

Now, isolate sin^2(x) on one side:

sin^2(x) = 1 - 5/8

To simplify, find a common denominator for 1 and 5/8:

sin^2(x) = 8/8 - 5/8

sin^2(x) = 3/8

So, sin^2(x) = 3/8.