Question

Вычислить: sin²x, если cos2x = 0.25

Answer 1

Cos2x = 0,25

1 - 2Sin²x = 0,25

2Sin²x = 0,75

Sin²x = 0,375

Answer 2

To find the value of sin²x when cos2x = 0.25, we can use a trigonometric identity that relates sin²x and cos²x:

sin²x + cos²x = 1

Also, there is another trigonometric identity that relates cos2x to cos²x and sin²x:

cos2x = cos²x - sin²x

Now, let's substitute the given value of cos2x = 0.25 into the second identity:

0.25 = cos²x - sin²x

Next, let's use the first identity to find cos²x:

cos²x = 1 - sin²x

Now, substitute this value of cos²x into the equation:

0.25 = 1 - sin²x - sin²x

Combine like terms:

0.25 = 1 - 2sin²x

Now, solve for sin²x:

2sin²x = 1 - 0.25

2sin²x = 0.75

sin²x = 0.75 / 2

sin²x = 0.375

So, the value of sin²x is 0.375.