Question

Решите sin(x)*cos(x)=-1

Answer 1

sinx • cosx = - 1

2sinx•cosx = sin2x - синус двойного аргумента

$\frac{1}{2}*2*sinx*cosx=-1\\\\\frac{1}{2}*sin2x=-1\\\\sin2x=-2$

Так как sint ∈ [ - 1 ; 1 ] , значит , корней нет.

ОТВЕТ: ∅

Answer 2

To solve the equation sin(x) * cos(x) = -1, we can use trigonometric identities to simplify the expression and find the values of x that satisfy the equation.

First, we can use the double-angle identity for sine: sin(2x) = 2 * sin(x) * cos(x). Rearranging this, we get:

sin(x) * cos(x) = (1/2) * sin(2x)

Now, we have the equation in terms of sin(2x):

(1/2) * sin(2x) = -1

Next, we can isolate sin(2x) by multiplying both sides by 2:

sin(2x) = -2

Now, we need to find the solutions for 2x. The sine function takes on values between -1 and 1, but it does not take on the value -2. This means there are no real solutions for 2x in this equation, and consequently, there are no real solutions for x either.

Therefore, the equation sin(x) * cos(x) = -1 has no real solutions.