1) To solve the equation 2cos x = √3, we first divide both sides by 2 to get cos x = √3/2. Then, we recall that cosine is positive in the first and fourth quadrants. In the first quadrant, the reference angle for cosine being √3/2 is π/6. Therefore, x = π/6.
2) To solve the equation tg x = √3, we first find the reference angle by taking the arctangent of √3, which is π/3. Since the tangent function is positive in the first and third quadrants, x can be π/3 or 4π/3.
3) To solve the equation ctg x = √3, we first find the reference angle by taking the arctangent of 1/√3, which is π/6. Then, we take the reciprocal of this value to get cotangent x = 1/(1/√3) = √3. Therefore, x can be π/6 or 5π/6.
1) To solve the equation 2cos x = √3, we first divide both sides by 2 to get cos x = √3/2. Then, we recall that cosine is positive in the first and fourth quadrants. In the first quadrant, the reference angle for cosine being √3/2 is π/6. Therefore, x = π/6.
2) To solve the equation tg x = √3, we first find the reference angle by taking the arctangent of √3, which is π/3. Since the tangent function is positive in the first and third quadrants, x can be π/3 or 4π/3.
3) To solve the equation ctg x = √3, we first find the reference angle by taking the arctangent of 1/√3, which is π/6. Then, we take the reciprocal of this value to get cotangent x = 1/(1/√3) = √3. Therefore, x can be π/6 or 5π/6.