Question

Sinx-cosx=1/√2 plz help me wit this problem

Answer 1

решение на листочке прикреплённом ===>>

Answer 2

Problem Statement

You are given the equation sin(x) - cos(x) = 1/√2 and you need to find the value of x that satisfies this equation.

Solution

To solve the equation sin(x) - cos(x) = 1/√2, we can use trigonometric identities to simplify the equation and find the value of x.

Let's start by rewriting the equation using the identity sin(x) = cos(π/2 - x):

cos(π/2 - x) - cos(x) = 1/√2

Next, we can use the identity cos(a) - cos(b) = -2sin((a+b)/2)sin((a-b)/2) to further simplify the equation:

-2sin((π/2 - x + x)/2)sin((π/2 - x - x)/2) = 1/√2

Simplifying the equation gives us:

-2sin(π/4)sin(-x/2) = 1/√2

Since sin(π/4) = 1/√2, we can simplify the equation further:

-2(1/√2)sin(-x/2) = 1/√2

Cancelling out the common factors gives us:

-sin(-x/2) = 1

Using the identity sin(-a) = -sin(a), we can rewrite the equation as:

sin(x/2) = 1

To find the value of x, we need to solve for x/2. Taking the inverse sine of both sides gives us:

x/2 = arcsin(1)

The inverse sine of 1 is equal to π/2, so we have:

x/2 = π/2

Multiplying both sides by 2 gives us the final solution:

x = π

Therefore, the value of x that satisfies the equation sin(x) - cos(x) = 1/√2 is π.

Please let me know if you need any further assistance.