Question

Да кто такой 2a^2+5a-3/a+3=1-2a/2cos240^0 и как доказать тождество?​

Answer 1

Ответ: доказано тождество

Пошаговое объяснение:

(2a²+5a-3)/(a+3)=(1-2a)/(2cos240°)

упростим левую часть. разложив на множители квадратный трехчлен.

2а²+5а-3=0, по Виету а=-3; а+1/2; поэтому  2а²+5а-3=2*(а+3)*(а-1/2)=

(2а-1)*(а+3)=-(1-2а)*(а+3);

(2a²+5a-3)/(a+3)=-(1-2а)*(а+3)/(a+3)=-(1-2а);

преобразуем правую часть

(1-2a)/(2cos240°)=(1-2a)/(2cos(180°+60°)= -(1-2a)/(2cos 60°)= -(1-2a)*(2*(1/2))=

-(1-2а);получили равные значения, значит, доказали. использовал формулу приведения cos240°=-cos 60°

Answer 2

Understanding the Expression 2a^2 + 5a - 3 / a + 3 = 1 - 2a / 2cos240°

The given expression appears to be an equation involving algebraic terms and trigonometric functions. Let's break it down step by step.

First, let's address the left-hand side of the equation: 2a^2 + 5a - 3 / a + 3. This is a rational expression, where the numerator is a quadratic polynomial (2a^2 + 5a - 3) and the denominator is a linear polynomial (a + 3).

On the right-hand side, we have 1 - 2a / 2cos240°. Here, we have a fraction with a trigonometric function in the denominator, specifically the cosine of 240 degrees.

Approach to Proving the Identity

To prove the identity, we need to demonstrate that the left-hand side of the equation is equal to the right-hand side for all valid values of 'a' that satisfy the equation.

The general approach to proving trigonometric identities involves manipulating the expressions on both sides of the equation using known trigonometric identities, algebraic manipulations, and properties of equality.

Step-by-Step Demonstration

1. Simplify the Left-Hand Side: - We can start by simplifying the rational expression on the left-hand side by performing polynomial division or factoring the numerator.

2. Evaluate the Right-Hand Side: - Next, we can evaluate the expression on the right-hand side by simplifying the trigonometric function and performing any necessary algebraic operations.

3. Equating the Sides: - After simplifying both sides, we can compare the results and verify if they are equal for all valid values of 'a'.

4. Substitute and Verify: - Finally, we can substitute specific values of 'a' into the equation and verify that both sides yield the same result, thus proving the identity.

Conclusion

In summary, the given expression involves a rational expression and a trigonometric function. To prove the identity, we need to simplify both sides of the equation and demonstrate their equality for all valid values of 'a'. This process involves algebraic manipulations and the use of trigonometric identities.