Some Famous Mathematical Formulaes

1)Area and Diagonals of a Cyclic Quadrilaterals
The Indians Brahmagupta and Mahavira gave the following formulae for the area and diagonal of a quadrilateral.
Area=Root of (s-a)(s-b)(s-c)(s-d) where a,b,c, and d are the sides of the quadrilateral and s is the semiperimeter; and diagonals are R of (ab+cd)(ac+bd)/(ad+bc) and Root of (ac+bd)(ad+bc)/(ab+cd)
The formulae are correct only for the cyclic quadrilaterals.
2)Sin(A+B)=sin A cos B+ cos A sin B
3)Aryabhatta in his Aryabhatiya discusses the method of solving (in integers)equations of the type:
N=ax+c=by=d or ax-by=k
4)The following is a general formula given by Mahavira:
N=[n(n-1)(n-2)...................
(n-r+1)]/1.2.3...........r
This occurs in verse 218 of his Ganitha Sara Sangraha
5)The following formula can be used to find out the sum of the first n consequtive counting numbers.
Sum=n(n+1)/2