Question

Sin^2 36° + cos^2 36° - tg^2 45 Cos60°sin30°-sin60°cos30°+cos120°tg135°

Answer 1

Ответ:

Sin^2 36° + cos^2 36° - tg^2 45 = 0;

Объяснение:

Поскольку , Основное тригонометрическое тождество :  sin2x + cos2x = 1

то выходит Sin^2 36° + cos^2 36° = 1;

Так же

tg^2 45 = 1 (можно посмотреть в таблице);

И поэтому выходит 1 - 1 = 0.

Answer 2

Let's break down the given expression step by step:

1. sin^2(36°) + cos^2(36°): The sum of the squares of the sine and cosine of any angle is always equal to 1. Therefore, sin^2(36°) + cos^2(36°) = 1.

2. -tg^2(45°): The tangent of 45° is equal to 1. Therefore, tg^2(45°) = 1^2 = 1.

Now let's simplify the second expression:

3. cos(60°)sin(30°) - sin(60°)cos(30°) + cos(120°)tg(135°):

First, let's evaluate each trigonometric function:

cos(60°) = 1/2 sin(30°) = 1/2 sin(60°) = √3/2 cos(30°) = √3/2 cos(120°) = -1/2 tg(135°) = tan(135°) = -1

Now we can substitute these values into the expression:

cos(60°)sin(30°) - sin(60°)cos(30°) + cos(120°)tg(135°) = (1/2)(1/2) - (√3/2)(√3/2) + (-1/2)(-1) = 1/4 - 3/4 + 1/2 = (1 - 3 + 2)/4 = 0/4 =

Therefore, the simplified expression is:

sin^2(36°) + cos^2(36°) - tg^2(45°) + cos(60°)sin(30°) - sin(60°)cos(30°) + cos(120°)tg(135°) = 1 - 1 + 0 = 0.