Question

Cosx(cosx+1) - sinx(cosx+1)=0 (cosx+1)*(cosx-sinx)=0 объясните пожалуйста как преобразовали

Answer 1

У Сosx и sinx общий множитель (cosx+1), поэтому Сosx - sinx взяли в скобки и умножили на их общий множитель. Надеюсь, понятно объяснила :)

Answer 2

Equation Transformation Explanation

To transform the given equation cos(x)(cos(x+1)) - sin(x)(cos(x+1)) = 0 into (cos(x+1))(cos(x-sin(x)) = 0, we can break down the steps as follows:

1. Factor out (cos(x+1)) from the equation: - The original equation can be rewritten as: (cos(x+1))(cos(x) - sin(x)) = 0. - This step involves factoring out the common factor (cos(x+1)) from both terms in the equation.

2. Simplify the expression: - After factoring out (cos(x+1)), the expression becomes (cos(x+1))(cos(x) - sin(x)) = 0.

3. Explanation of the transformation: - By factoring out (cos(x+1)) from the original equation, we can rewrite the equation in a simplified form, which is (cos(x+1))(cos(x) - sin(x)) = 0. This transformation allows us to clearly see that the equation is the product of two factors, where one of the factors is (cos(x+1)) and the other factor is (cos(x) - sin(x)).

This transformation simplifies the equation and allows for easier analysis of the individual factors and their implications for the solutions of the original equation.