Determine the angle a for arcsina + arcos1/2 = pi.

 arc sina+ arxco(1/2) =
pi.

We know that sin(A+B) = sinAcosB+cosAsinB
.

Therfore taking sine of both sides ofthe given equation,
we get:

 sin (arcsina) cos(arccos(1/2) +cos(arc sina) sin(
arc cos(1/2) ) = sin pi = 0.

a* (1/2) -
sqrt(1-a^2)sqrt{1-(1/2)^2} = 0.

a/2 +sqrt(1-a^2)*(sqrt3/2)
= 0

 a /2=
-(1/2)sqrt(1-a^2)*sqrt3

a =
-sqrt(1-a^2)*sqrt3

a^2 =
3(1-a^2)

a^2 =
3-3a^2

4a^2=3

a^2 =
3/4

a = +sqrt3/2. Or a =
-sqrt3/2

Therefore angles are :  Therfore arc  sqrt
sinsqrt3/2 = 120 and arc cos(1/2) = 60.

Also a = 240 degree
and arc cos (1/2) = -60 deg