Question

ДАЮ 40 БАЛЛОВ! Решите пример №3. cos ^2 x + sin x · cos x = 1 Р е ш е н и е . cos ^2 x + sin x · cos x – sin 2 x – cos ^2 x = 0 , Дорешать!

Answer 1

только разбертсь прежде чем списывать

Answer 2

Solving the Equation

To solve the given equation cos^2(x) + sin(x) * cos(x) = 1, we can use trigonometric identities and algebraic manipulation to simplify and solve for the value of x.

First, let's rewrite the given equation in terms of sine and cosine using the identity sin^2(x) + cos^2(x) = 1.

The equation becomes: cos^2(x) + sin(x) * cos(x) - sin^2(x) - cos^2(x) = 0

Now, let's simplify the equation by combining like terms: - sin^2(x) + cos^2(x) + sin(x) * cos(x) - cos^2(x) = 0

Simplifying further: - sin^2(x) + sin(x) * cos(x) = 0

Now, we have a quadratic equation in terms of sine and cosine. We can use substitution to simplify it further.

Let's substitute sin(x) = u and cos(x) = v. Then, the equation becomes: -u^2 + u * v = 0

We can solve for u in terms of v: u * (v - u) = 0

This equation implies that either u = 0 or v = u.

Now, we can substitute back the values of u and v to find the solutions for x.

Conclusion

The solutions for the equation cos^2(x) + sin(x) * cos(x) = 1 are based on the trigonometric identities and algebraic manipulation. By simplifying the given equation and using substitution, we can find the values of x that satisfy the equation.