Question

8sinxcosx=0Помогите срочно!!!

Answer 1

$8sinxcosx=0 \\ \\ \left [\begin{array}{I} sinx=0 \\ cosx=0 \end{array}$

$\left [\begin{array}{I} x= \pi k;\ k \in Z\\ x= \dfrac{ \pi }{2}+ \pi k;\ k \in Z \end{array}$

Answer 2

Solving the Equation 8sin(x)cos(x) = 0

To solve the equation 8sin(x)cos(x) = 0, we can use the trigonometric identity that states: sin(2x) = 2sin(x)cos(x). This identity will help us simplify the given equation and find the solutions for x.

Using the identity, we can rewrite the equation as: 8sin(x)cos(x) = 0 4(2sin(x)cos(x)) = 0 4sin(2x) = 0

Now, we can solve for x by finding the values of 2x that satisfy the equation 4sin(2x) = 0.

The solutions for sin(2x) = 0 occur when 2x = kπ, where k is an integer.

Therefore, the solutions for x are: 2x = kπ x = kπ/2

So, the solutions for the equation 8sin(x)cos(x) = 0 are x = kπ/2, where k is an integer.

This means that the solutions for x are all the multiples of π/2.

I hope this helps! If you have any further questions, feel free to ask.