Question

4)3-sin^2(-π/3)-cos^2(-π/3)/2cos(-π/4)=

Answer 1

3 - sin²(-π/3) - cos²(-π/3) / 2cos(-π/4)

Подставляя значения таблицы получим:

sin²(-π/3) = (-√3/2)²=3/4=0,75

cos²(-π/3) = (1/2)²=1/4=0,25

2cos(-π/4) = 2 * √2/2=√2

Вычислим:

3 - 0,75 - 0,25/√2 = 2,25 - √2/8

Answer 2

Let's break down the expression step by step:

1. Evaluate sin^2(-π/3): Since sin(-π/3) = -√3/2, then sin^2(-π/3) = (-√3/2)^2 = 3/4.

2. Evaluate cos^2(-π/3): Since cos(-π/3) = 1/2, then cos^2(-π/3) = (1/2)^2 = 1/4.

3. Evaluate cos(-π/4): Since cos(-π/4) = cos(π/4) and cos(π/4) = √2/2, then cos(-π/4) = √2/2.

Now, substitute the values back into the expression:

(3 - 3/4 - 1/4) / (2 * √2/2)

Now simplify:

(12/4 - 3/4 - 1/4) / √2

(8/4) / √2

2 / √2

To rationalize the denominator, multiply both the numerator and denominator by √2:

(2 / √2) * (√2 / √2)

(2√2) / 2

Cancel out the common factor of 2:

√2

So, the simplified expression is √2.