Question

Arcsin(-корень 3/2)+2 arcsin (-1/2)

Answer 1

=2*пи\3+sin пи\ 4=2*пи\3+1

Answer 2

We can start by using the identity:

arcsin(x) + arcsin(y) = arcsin(x sqrt(1-y^2) + y sqrt(1-x^2))

to simplify the expression. Applying this identity, we get:

arcsin(-корень 3/2) + 2arcsin(-1/2) = arcsin(-корень 3/2) + arcsin(-1/2) + arcsin(-1/2)

Now, let's use the identity:

arcsin(-x) = -arcsin(x)

to simplify the first term. We get:

arcsin(-корень 3/2) = -arcsin(корень 3/2)

Next, we can use the fact that:

sin(arcsin(x)) = x

to simplify the remaining terms. We get:

• arcsin(корень 3/2) + arcsin(-1/2) + arcsin(-1/2) = - arcsin(корень 3/2) + π/6 + π/6 [using the fact that sin(π/6) = 1/2]

= - arcsin(корень 3/2) + π/3

Therefore, the final answer is:

arcsin(-корень 3/2) + 2arcsin(-1/2) = - arcsin(корень 3/2) + π/3.