Question

Вычислите sin45+cos135-tg120

Answer 1

√2/2–√2/2–√3=–√3
tg120=√3/2:1/2=√3

Answer 2

I can help you with math problems. Here is the solution to your question:

To find the value of $$sin45 \cdot cos135 - tg120$$, we need to use the following trigonometric identities:

$$sin(a+b) = sin(a) \cdot cos(b) + cos(a) \cdot sin(b)$$ $$cos(a+b) = cos(a) \cdot cos(b) - sin(a) \cdot sin(b)$$ $$tg(a+b) = \frac{tg(a) + tg(b)}{1 - tg(a) \cdot tg(b)}$$

Using these identities, we can rewrite the given expression as follows:

$$sin45 \cdot cos135 - tg120 = sin(45) \cdot cos(90 + 45) - tg(90 + 30)$$ $$= sin(45) \cdot (cos(90) \cdot cos(45) - sin(90) \cdot sin(45)) - \frac{tg(90) + tg(30)}{1 - tg(90) \cdot tg(30)}$$

Next, we need to use the values of the trigonometric functions at some common angles. These values can be found in a trigonometric table or derived from the unit circle. Here are the values that we need:

$$sin(45) = cos(45) = \frac{\sqrt{2}}{2}$$ $$sin(90) = 1$$ $$cos(90) = 0$$ $$tg(90) = \text{undefined}$$ $$tg(30) = \frac{\sqrt{3}}{3}$$

Substituting these values into the expression, we get:

$$sin45 \cdot cos135 - tg120 = \frac{\sqrt{2}}{2} \cdot (0 \cdot \frac{\sqrt{2}}{2} - 1 \cdot \frac{\sqrt{2}}{2}) - \frac{\text{undefined} + \frac{\sqrt{3}}{3}}{1 - \text{undefined} \cdot \frac{\sqrt{3}}{3}}$$ $$= -\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} - \frac{\text{undefined} + \frac{\sqrt{3}}{3}}{1 - \text{undefined} \cdot \frac{\sqrt{3}}{3}}$$ $$= -\frac{1}{2} - \frac{\text{undefined} + \frac{\sqrt{3}}{3}}{1 - \text{undefined} \cdot \frac{\sqrt{3}}{3}}$$

The last term in the expression is undefined, because it involves dividing by zero. Therefore, the final answer is also undefined. We can write this as:

$$sin45 \cdot cos135 - tg120 = \text{undefined}$$

This means that there is no real number that satisfies the given expression.

I hope this helps you understand the problem. If you need more help with math, you can visit [Mathway](https://www.mathway.com/trigonometry), a free online math solver. You can also find more trigonometric identities and formulas at [Socratic](https://socratic.org/questions/how-do-you-write-the-trigonometric-form-into-a-complex-number-in-standard-form-4).