Question

Помогите решить пример:

Answer 1

Sin2xCosx + Cos2xSinx = 0
2SinxCosxCosx + Cos2xSinx = 0
Sinx(2Cos²x + Cos2x) = 0
Sinx(2Cos²x + 2Cos²x - 1) = 0
Sinx(4Cos²x - 1) = 0
Sinx = 0                                          4Cos²x -1= 0
x = πn , n ∈ z                                  4Cos²x = 1
                                                        Cos²x = 1/4
$Cosx = \frac{1}{2}$                              $Cosx = - \frac{1}{2}$
$x = + - \frac{ \pi }{3} +2 \pi n$,n∈z       $x = + - \frac{2 \pi }{3} +2 \pi n,$n∈z

Answer 2

Problem:

The problem is to solve the expression: tg 720 + sin 540 - ctg 135.

Solution:

To solve the expression, we can break it down into individual trigonometric functions and evaluate them separately. Let's break down the expression step by step:

1. tg 720: According to the search result snippet from Source tg 720 is equal to tg 360, which is equal to tg 0, which is equal to 0.

2. sin 540: According to the search result snippet from Source sin 540 is equal to sin 180, which is equal to 0.

3. ctg 135: According to the search result snippet from Source ctg 135 is equal to ctg(90 + 45), which is equal to -tg 45, which is equal to -1.

Now, let's substitute these values back into the original expression:

tg 720 + sin 540 - ctg 135 = 0 + 0 - (-1) = 0 + 0 + 1 = 1.

Therefore, the solution to the expression tg 720 + sin 540 - ctg 135 is 1.

Please let me know if you need any further assistance!