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Qus. Algebra: What is algebra?
Algebra may divided into "classical algebra" (equation solving or "find the unknown number" problems) and "abstract algebra", also called "modern algebra" (the study of groups, rings, and fields). Classical algebra has been developed over a period of 4000 years. Abstract algebra has only appeared in the last 200 years. The development of algebra is outlined in these notes under the following headings: Egyptian algebra, Babylonian algebra, Greek geometric algebra, Diophantine algebra, Hindu algebra, Arabic algebra, European algebra since 1500, and modern algebra. Since algebra grows out of arithmetic, recognition of new numbers - irrationals, zero, negative numbers, and complex numbers - is an important part of its history. The development of algebraic notation progressed through three stages: the rhetorical (or verbal) stage, the syncopated stage (in which abbreviated words were used), and the symbolic stage with which we are all familiar.

Qus. Trigonometry: Solve Sin 75 cos 15 + cos 75 sin 15 =?
sin (A+B) = sin A cos B + cos A sin B
Here A = 75 and B = 15
Therefore sin 75 cos 15 + cos 75 sin 15 = sin (75 + 15)
= sin 90
= 1

Qus. Algebra: Find the sum of numbers from 1 to 100.
formula for finding sum up to given limit from 1 is

sum=n*(n+1)/2
n=100
sum=100*(100+1)/2
=5050

Qus. Algebra: What does '!' mean in maths?