cant find the value of x from a equation.

Question

how can i find the value of x??

Answer 1

I suggest working with inverse trig functions, in this case, the arcsine.

a = sin[(a + x) / 2] / sin(a/2)

a sin(a/2) = sin[(a + x) / 2]

arcsin[a sin(a/2)] = arcsin{sin[(a + x) / 2]}

arcsin[a sin(a/2)] = (a + x) / 2

x = 2 arcsin[a sin(a/2)] - a

Now here is where you can run into trouble. The arcsine is multivalued. You might need a domain restriction, or something else.