Question

Cos x + sin^2 x = -cos^2 x

Answer 1

Просто перепиши и будет тебе радость

Answer 2

Let's solve the equation cos(x) + sin^2(x) = -cos^2(x) for x.

First, let's work with the equation and manipulate it:

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

We know that sin^2(x) + cos^2(x) = 1 (the Pythagorean identity). Therefore, we can replace sin^2(x) with 1 - cos^2(x):

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

Now, simplify:

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

Next, move all the terms to one side of the equation:

cos(x) + 1 - cos^2(x) + cos^2(x) = 0

Now, combine the cos^2(x) terms:

cos(x) + 1 = 0

Subtract 1 from both sides:

cos(x) = -1

Now, we need to find the values of x that satisfy cos(x) = -1. In the unit circle, cos(x) is equal to -1 when x is an odd multiple of π (pi):

x = π + 2πn, where n is an integer.

So, the solution for x is:

x = π(1 + 2n), where n is an integer.

This represents a family of solutions where x can be any odd multiple of π.