Question

Cos^2(pi/2+x)-cos^2(2pi+x)=под корнем 3/2

Answer 1

Получится вот так :)

Answer 2

To solve the given equation:

cos^2(pi/2 + x) - cos^2(2pi + x) = √(3/2)

Let's simplify the equation step by step:

Using the identity cos^2(x) = 1 - sin^2(x), we can rewrite the equation as:

1 - sin^2(pi/2 + x) - (1 - sin^2(2pi + x)) = √(3/2)

Simplifying further:

1 - sin^2(pi/2 + x) - (1 - sin^2(x)) = √(3/2)

Now, let's simplify the trigonometric expressions:

1 - cos^2(x) - (1 - sin^2(x)) = √(3/2)

Expanding and simplifying:

1 - cos^2(x) - 1 + sin^2(x) = √(3/2)

Combining like terms:

sin^2(x) - cos^2(x) = √(3/2)

Using the trigonometric identity sin^2(x) - cos^2(x) = -cos(2x), we have:

-cos(2x) = √(3/2)

Now, divide both sides of the equation by -1:

cos(2x) = -√(3/2)

Taking the square root of both sides:

2x = arccos(-√(3/2))

Now, divide both sides by 2:

x = (1/2) * arccos(-√(3/2))

Please note that the value of x can be further simplified or expressed in terms of radicals, depending on the desired form.