sin square a-sin square b+ sin square c=2sinacosbsinc
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LHS=sin²a+sin²b-sin²c
Applying addition formula
sin (A+B)Sin(A-B)=Sin²Α-Sin²Β
Sin²a+Sin²b-Sin²c=Sin²a+Sin(b+c)Sin(b-c)
=Sin²a+Sin(π−a)Sin (b-c)
= Sin²a+Sin a Sin(b-c)
= Sin a{Sin a+Sin (b-c)}
= Sin a[2Sin {(a+b-c)/2}Cos{(a-b+c)/2}]
= 2Sin a[Sin {(π/2)-c} Cos{(π/2)-b}]
= 2Sin aCosc Sin b
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