Question

Sin(arccos(корень 3/2)+arcsin (корень3/2))

Answer 1

$sin(arccos( \sqrt{3}/2)+arcsin ( \sqrt{3}/2)) =$
$= sin( \frac{ \pi }{6} + \frac{ \pi }{3} ) = sin \frac{ \pi }{2} = 1$

Answer 2

To simplify the given expression, let's break it down step by step:

1. Let's start with the innermost part: arccos(корень 3/2). Since корень 3/2 means the square root of 3 divided by 2, we can rewrite the expression as arccos(sqrt(3)/2).

2. We can use the identity arccos(x) + arcsin(x) = pi/2 for any valid value of x. In this case, x = sqrt(3)/2, so we have arccos(sqrt(3)/2) + arcsin(sqrt(3)/2) = pi/2.

3. Substituting the value of arccos(sqrt(3)/2) + arcsin(sqrt(3)/2) with pi/2, we have sin(pi/2).

4. The value of sin(pi/2) is 1.

Therefore, the simplified expression Sin(arccos(корень 3/2)+arcsin (корень3/2)) evaluates to 1.