Question

Tg(2x+pi/3)=1 решать

Answer 1

Ответ:

2x+pi/3=pi/4+pik

2x=-pi/12+pik

x=-pi/24 +pik/2

ответ:11pi/24+pik/2

Пошаговое объяснение:

Answer 2

To solve the equation Tg(2x + π/3) = 1, we can follow these steps:

Step 1: Rewrite the equation in terms of sine and cosine. Since tangent (Tg) is equal to sine (sin) divided by cosine (cos), we can express the equation as sin(2x + π/3) / cos(2x + π/3) = 1.

Step 2: Use the trigonometric identity for tangent. The identity for tangent is sin(x) / cos(x), so we can rewrite the equation as sin(2x + π/3) = cos(2x + π/3).

Step 3: Apply the double-angle formulas. Using the double-angle formulas, we have sin(2x + π/3) = cos(π/2 - (2x + π/3)). Simplifying the right side gives cos(π/6 - 2x).

Step 4: Apply the angle addition formula for cosine. Using the angle addition formula for cosine, we have cos(π/6 - 2x) = cos(π/6)cos(2x) + sin(π/6)sin(2x).

Step 5: Simplify and solve for x. Comparing the equation obtained in step 4 with the equation in step 3, we can equate the corresponding terms: cos(2x + π/3) = cos(π/6)cos(2x) + sin(π/6)sin(2x).

Using the identity cos(π/6) = √3/2 and sin(π/6) = 1/2, we have: cos(2x + π/3) = (√3/2)cos(2x) + (1/2)sin(2x).

Now, you can solve the equation by equating the corresponding coefficients of cosine and sine terms and solving for x.