Eliminate `x` from equations `sin(a+x)=2b` and `sin(a-x)=2c`.

Explanation

On adding we get,
`sin (a+x)+sin(a-x)=2(b+c)`
`2sin a cosx=2(b+c)`
or `cos x=(b+c)/(sin a)`
On subtracting we get
`sin(a+b)-sin(a-x)=2(b-c)`
or `2cos a sin xjj=2(b-c)`
or `sin x=(b-c)/(cos a)`
Squaring and adding Eqs. (i) and (ii), we get
`((b+c)^(2))/(sin^(2)a)+((b-c)^(2))/(cos^(2)a(=1`