Question

√2sin45° +√2tg135° -cos150°

Answer 1

$\sqrt{2 \sin(45) } + \sqrt{2 \tan(135) } - \cos(150)$

$\sqrt{2 \tan(135) }$

по таблице tg135°, это -1

√2×(-1)=√-2

квадратный корень из отрицательного числа не извлекается

Answer 2

Let's calculate each part separately and then combine them:

1. √2sin(45°): sin(45°) is equal to √2/2, so √2sin(45°) = √2 * (√2/2) = 2/2 = 1.

2. √2tg(135°): tg(135°) is the tangent of 135°, which is equal to -1. So, √2tg(135°) = √2 * (-1) = -√2.

3. -cos(150°): cos(150°) is the cosine of 150°. You can find the cosine of an angle by subtracting it from 180° and then finding the cosine of the result: cos(150°) = cos(180° - 150°) = cos(30°).

   The cosine of 30° is √3/2, so cos(150°) = √3/2.

Now, let's add these values together: 1 + (-√2) - (√3/2)

To combine them, let's get a common denominator, which is 2: 2/2 - √2 - (√3/2)

Now, we can add the fractions: (2 - √2 - √3) / 2

So, the final result is (2 - √2 - √3) / 2.