Question

Sin²120°-cos²0°cos45°sin135°ctg45°ctg²60°+sin²30°

Answer 1

Ответ на первый пример
там где написано cot это ctg
по табличному значению
$\cot(60) = \frac{ \sqrt{3} }{3}$
и это возводим в квадрат
$({ \frac{ \sqrt{3} }{3} })^{2} = \frac{3}{9} = \frac{1}{3}$
$\sin(30) = \frac{1}{2}$
возводим в квадрат
$( { \frac{1}{2} })^{2} = \frac{1}{4}$
соединяем
$\frac{1}{3} + \frac{1}{4} = \frac{7}{12}$

Answer 2

Let's simplify the given expression step by step:

1. Convert all trigonometric functions to their corresponding values:

• sin(120°) = √3/2
• cos(0°) = 1
• cos(45°) = √2/2
• sin(135°) = √2/2
• ctg(45°) = 1 (Note: cotangent is the reciprocal of tangent)
• ctg(60°) = 1/√3
• sin(30°) = 1/2

2. Substitute the values into the expression:

sin²(120°) - cos²(0°) * cos(45°) * sin(135°) * ctg(45°) * ctg²(60°) + sin²(30°)

= (√3/2)² - 1² * (√2/2) * (√2/2) * 1 * (1/√3)² + (1/2)²

= (3/4) - 1 * (1/2) * (1/2) * (1/3) + 1/4

3. Simplify the expression further:

= 3/4 - 1/12 + 1/4

4. Find a common denominator and combine the fractions:

= (9/12) - (1/12) + (3/12)

= 11/12

So, the simplified value of the expression is 11/12.