Question

Tg^45° * cos 30° * ctg^ 30=

Answer 1

Tg^45° * cos 30° * ctg^ 30=1*√3/2*√3=3/2

Answer 2

To simplify the expression, let's use the trigonometric identities:

1. Tangent Double Angle Identity: tan(2θ) = (2 * tan(θ)) / (1 - tan^2(θ))

2. Cotangent Identity: cot(θ) = 1 / tan(θ)

Now, let's proceed step-by-step:

1. Tg^45°: Tg^45° is equivalent to tan^45°. Using the tangent double angle identity with θ = 45°: tan(2 * 45°) = (2 * tan(45°)) / (1 - tan^2(45°))

But we know that tan(45°) = 1, so the expression becomes: (2 * 1) / (1 - 1^2) = 2 / 0

2. cos 30°: cos(30°) is the cosine of 30 degrees. The value of cos(30°) is √3/2 ≈ 0.8660254.

3. ctg^30: ctg^30 is equivalent to cot^30°. Using the cotangent identity with θ = 30°: cot(30°) = 1 / tan(30°)

But we know that tan(30°) = √3/3, so the expression becomes: 1 / (√3/3) = √3/3 ≈ 0.5773503.

Now, putting it all together:

Tg^45° * cos 30° * ctg^30 = (2 / 0) * (√3/2) * (√3/3)

Since division by zero is undefined, the entire expression is undefined.