Question

rozwiąż dwa równania: 1. (2 cosx-1) * (2 cosx+1) = 3 ||| 2. 3sin^2x - cos^2x = 1

Answer 1

1.

(2 cosx-1) * (2 cosx+1) = 3

4cos²x - 1 = 3

4cos²x = 4    /:4

cos²x = 1

cosx = 1         lub     cosx =-1

x1 = 0 + 2kπ            x3 = π  + 2kπ

x2 = 2π + 2kπ

 

odp. x = kπ  gdzie k ∈ C

 

 

2.

3sin^2x - cos^2x = 1

3sin²x - (1 - sin²x) = 1

3sin²x - 1 + sin²x = 1

4sin²x = 2    /:4

sin²x = 1/2

sinx = √2/2                    lub             sinx = -√2/2

x1 = π/4 + 2kπ                                   x3 = (π + π/4) + 2kπ = 5π/4 + 2kπ

x2 = (π - π/4) + 2kπ = 3π/4 + 2kπ       x4 = (2π - π/4) + 2kπ = 7π/4 + 2kπ     gdzie k ∈ C