Question

Sin(x)+cos(x)+sin(x)*cos(x)=1 x-?

Answer 1

Ответ:

Объяснение:Возведём обе части уравнения в квадрат,  

sinx*sinx+cosx*cosx -2sinx*cosx=1  

Первые два слагаемых в сумме дают единицу:  

1-2sinx*cosx=1  

2sinx*cosx=0  

sinx*cosx=0  

Теперь, произведение равно 0, когда один из множителей равен 0  

Если sin x = 0, то из уравнения получаем cos x = -1

 

Объяснение:

Answer 2

To find the value of 'x' that satisfies the equation Sin(x) + Cos(x) + Sin(x) * Cos(x) = 1, we can start by manipulating the equation:

Sin(x) + Cos(x) + Sin(x) * Cos(x) = 1

Let's express Sin(x) * Cos(x) as a single term using the trigonometric identity:

Sin(x) * Cos(x) = (1/2) * 2 * Sin(x) * Cos(x) = (1/2) * Sin(2x)

Now the equation becomes:

Sin(x) + Cos(x) + (1/2) * Sin(2x) = 1

To simplify it further, let's express Sin(2x) in terms of Sin(x) and Cos(x) using the double angle formula:

Sin(2x) = 2 * Sin(x) * Cos(x)

Now the equation becomes:

Sin(x) + Cos(x) + (1/2) * (2 * Sin(x) * Cos(x)) = 1

Combine the like terms:

Sin(x) + Cos(x) + Sin(x) * Cos(x) = 1

Now, we have a similar term on both sides of the equation (Sin(x) * Cos(x)). To simplify it even further, we can add Sin(x) * Cos(x) to both sides and then factor out the common term:

Sin(x) + Cos(x) + Sin(x) * Cos(x) + Sin(x) * Cos(x) = 1 + Sin(x) * Cos(x)

2 * Sin(x) * Cos(x) + Sin(x) + Cos(x) = 1 + Sin(x) * Cos(x)

Now, subtract Sin(x) * Cos(x) from both sides:

2 * Sin(x) * Cos(x) + Sin(x) + Cos(x) - Sin(x) * Cos(x) = 1

Combine the terms on the left side:

2 * Sin(x) * Cos(x) + Sin(x) + Cos(x) - Sin(x) * Cos(x) = 1

2 * Sin(x) * Cos(x) - Sin(x) * Cos(x) + Sin(x) + Cos(x) = 1

Sin(x) + Cos(x) = 1

Now, we have a new equation:

Sin(x) + Cos(x) = 1

To solve this equation, we can use the fact that the maximum value of Sin(x) + Cos(x) is √2, and the minimum value is -√2. Since we want the result to be 1, we can set up the equation:

√2 * Sin(x) + √2 * Cos(x) = 1

Now, divide both sides by √2:

Sin(x) + Cos(x) = 1/√2

To find the value of x that satisfies this equation, we can use the unit circle or trigonometric tables. One possible solution for x is:

x = π/4 (45 degrees)

This is because at x = π/4, Sin(x) and Cos(x) are both equal to 1/√2, which satisfies the equation Sin(x) + Cos(x) = 1/√2.

There are multiple solutions to this equation due to the periodic nature of the trigonometric functions. For example, x = 5π/4, x = 9π/4, etc., are also solutions. These are additional angles in the unit circle where Sin(x) + Cos(x) equals 1/√2.