Question

Cos60°+2sin30°+1/2tg60°-ctg45°

Answer 1

Ответ:

Пошаговое объяснение:

cos60°+2sin30°+1/2tg60°-ctg45°

cos60° = 0.5

2sin30°=2*0.5 =1

1/2tg60° = 1/2 * 1.73 = 1/ 3.46= 0.29

ctg45°= 1

Итого = 0,5 +1+0,29 +1 = 2,79

Answer 2

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

1. cos(60°): Using the value of cosine for 60 degrees, which is 1/2: cos(60°) = 1/2

2. 2sin(30°): Using the value of sine for 30 degrees, which is 1/2: 2sin(30°) = 2 * (1/2) = 1

3. 1/2tan(60°): To simplify this term, let's find the value of tangent for 60 degrees: tan(60°) = √3 Therefore: 1/2tan(60°) = 1/2 * √3 = √3/2

4. csc(45°): The reciprocal of sine is cosecant (csc). The value of sine for 45 degrees is 1/√2. csc(45°) = 1 / (1/√2) = √2

Now let's substitute the simplified values back into the expression:

cos(60°) + 2sin(30°) + 1/2tan(60°) - csc(45°) = 1/2 + 2 * 1 + √3/2 - √2

To simplify further, we can rationalize the denominator of the last term:

= 1/2 + 2 + √3/2 - √2 * (√2/√2) = 1/2 + 2 + √3/2 - 2/√2

Now let's rationalize the denominator of the last term:

= 1/2 + 2 + √3/2 - (2/√2) * (√2/√2) = 1/2 + 2 + √3/2 - 2√2/2 = 1/2 + 2 + √3/2 - √2

Combining like terms:

= (1 + 2) + (1/2 + √3/2 - √2) = 3 + (1 + √3 - √2)/2

Therefore, the simplified expression is 3 + (1 + √3 - √2)/2.