Question

2cos(arccos√2/2)+4sin(arcsin√2/2)=?

Answer 1

Ответ:

2cos(45) + 4sin(45) = 2*корень2 \2 + 4*корень2 \2 = 3* корень2

Answer 2

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

1. Recall that the cosine of the angle whose cosine is √2/2 is π/4 radians or 45 degrees. So, arccos(√2/2) = π/4.

2. Similarly, the sine of the angle whose sine is √2/2 is also π/4 radians or 45 degrees. So, arcsin(√2/2) = π/4.

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

2cos(arccos(√2/2)) + 4sin(arcsin(√2/2))

Since cos(arccos(x)) = x and sin(arcsin(x)) = x for all valid values of x:

2 * (√2/2) + 4 * (√2/2)

Simplify the terms:

√2 + 2√2

Combine like terms:

3√2

So, 2cos(arccos(√2/2)) + 4sin(arcsin(√2/2)) simplifies to 3√2.