Question

2sin pi/3×cos pi/6-1/2tg^2pi/3

Answer 1

Ответ:

2sin⁡〖π/3〗  cos⁡〖π/6〗-1/2  tg^2⁡〖π/3〗=2*√3/2*√3/2-1/2*√3=3/2-3/2=0

Пошаговое объяснение:

Answer 2

To simplify the expression, let's break it down step by step:

1. Start with the given expression: 2sin(pi/3) × cos(pi/6) - 1/2tan^2(pi/3).

2. Recall the values of sine and cosine for the given angles:

   • sin(pi/3) = √3/2
   • cos(pi/6) = √3/2

3. Substitute these values into the expression: 2(√3/2) × (√3/2) - 1/2tan^2(pi/3).

4. Simplify the first part of the expression: 2(√3/2) × (√3/2) = 3/2.

5. Simplify the second part of the expression: tan(pi/3) = sin(pi/3) / cos(pi/3) = (√3/2) / (1/2) = √3.

   tan^2(pi/3) = (√3)^2 = 3.

   Therefore, -1/2tan^2(pi/3) = -1/2(3) = -3/2.

6. Substitute the simplified values back into the expression: 3/2 - 3/2 = 0.

Thus, the final result of the expression 2sin(pi/3) × cos(pi/6) - 1/2tan^2(pi/3) is 0.