Question

Cos(П/2 + х) * ctg П/4 * ctg(П/2 - L) / tg(П+L) * sin(2П+х)​

Answer 1

$\dfrac{cos\Big(\dfrac{\pi}{2}+x\Big)\cdot ctg\dfrac{\pi}{4}\cdot ctg\Big(\dfrac{\pi}{2}-L\Big)}{tg(\pi +L)\cdot sin(2\pi+x)}=\dfrac{-sinx\cdot 1\cdot tgL}{tgL\cdot sinx}=-1$

Answer 2

It seems like you've provided a mathematical expression involving trigonometric functions. Let's break down the expression step by step:

1. Cos(П/2 + х): This represents the cosine function of the angle (π/2 + x), where x is a variable.

2. ctg П/4: This seems to be a notation for the cotangent function. ctg(π/4) is equivalent to 1. The cotangent of π/4 is 1.

3. ctg(П/2 - L): This represents the cotangent function of the angle (π/2 - L), where L is a variable.

4. tg(П+L): This represents the tangent function of the angle (π + L), where L is a variable.

5. sin(2П+х): This represents the sine function of the angle (2π + x), where x is a variable.

So, the entire expression can be written as:

$\frac{\cos(\frac{\pi}{2} + x) \cdot \cot(\frac{\pi}{4}) \cdot \cot(\frac{\pi}{2} - L)}{\tan(\pi + L) \cdot \sin(2\pi + x)}$

However, please note that some of these trigonometric identities involve undefined values or specific cases. For instance, the denominator $\tan(\pi + L)$ would be undefined when $\pi + L$ is an odd multiple of $\pi$, because the tangent function is undefined at those points.

If you're looking for a specific simplification or evaluation of this expression, please provide specific values for the variables $x$ and $L$, or let me know what you're trying to achieve with this expression.