Question

Ctg(2x+45°)=-1

Answer 1

ctg(2x+45°)=-1

2x+45°=-45°+180° *k

2x=90°+180° *k

x=45°+90° *k,где  k  -целое

ответ: 45°+90° *k,где  k  -целое

Answer 2

To find the value of x that satisfies the equation ctg(2x + 45°) = -1, we'll need to use trigonometric identities and solve for x.

The reciprocal of the cotangent function is the tangent function, so we can rewrite the equation as:

tan(2x + 45°) = -1

To solve this equation, we can use the inverse tangent function (arctan) to isolate x:

2x + 45° = arctan(-1)

Now, we need to find the angle whose tangent is -1. This occurs in the third quadrant, where the tangent is negative. In the third quadrant, the reference angle with a tangent of 1 is 45 degrees.

So, we have:

2x + 45° = 180° - 45°

Simplifying further:

2x = 135°

Dividing both sides by 2:

x = 67.5°

Therefore, the solution to the equation ctg(2x + 45°) = -1 is x = 67.5°.