Question

Sin(23n+2018)+cos(31n/2+2018)=​

Answer 1

Ответ:

Раскрываем по формуле (Sin23nCos2018+Cos23nSin2018)+(Cos Cos31n/2Cos2018-Sin31n/2Sin2018)

Answer 2

The equation you've provided involves trigonometric functions and an integer variable "n." To solve this equation for specific values of "n," you can use trigonometric identities and properties. However, if you're looking for a general solution in terms of "n," it might not be possible to find an exact closed-form solution, and you may need to resort to numerical methods or approximations.

Let's break down the equation step by step:

1. Sin(23n + 2018) + cos(31n/2 + 2018) = 0

First, we can apply the trigonometric identity: cos(a) = sin(π/2 - a) to the second term:

2. Sin(23n + 2018) + sin(π/2 - (31n/2 + 2018)) = 0

3. Sin(23n + 2018) + sin((π - 31n)/2 - 2018) = 0

Now, let's use the sum-to-product trigonometric identity: sin(x) + sin(y) = 2 * sin((x + y)/2) * cos((x - y)/2):

4. 2 * sin((23n + 2018 + (π - 31n)/2 - 2018)/2) * cos((23n + 2018 - (π - 31n)/2 + 2018)/2) = 0

5. sin((23n + π - 31n)/4) * cos((54n + π)/4) = 0

6. sin((-8n + π)/4) * cos((54n + π)/4) = 0

7. sin(-2n + π/4) * cos(54n + π/4) = 0

At this point, we have an equation in terms of the sine and cosine functions of specific angles. The equation will be satisfied if either of the two factors is equal to zero:

Factor 1: sin(-2n + π/4) = 0 -2n + π/4 = k * π, where k is an integer

Factor 2: cos(54n + π/4) = 0 54n + π/4 = (2k + 1) * π/2, where k is an integer

Solve each of these equations for "n" to find the possible values of "n" that satisfy the original equation.

Please note that finding a general solution in terms of "n" might be complex and involve solving transcendental equations. If you're looking for specific solutions or more information, you might need to provide additional context or constraints for the equation.