write squares of numbers

you can keep on writing squares of natural numbers from 1. Write 1 and to its right sq. of 1. Go to next line write next number i.e. 2 below first '1' written. Now add to 1 written in square column number written in natural number column. Add the latest number written in natural number column to the previous sum. Continue like this till you want.
algebra behind:
( a + 1) sq = a sq + 2a +1 = a sq + a + ( a + 1 )

Trigonometry

Trigonometry:
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The first letter of every word can be used to remember the 3 basic trigonometric ratios of sine, cosine & tangent.
Opposite side / Hypotenuse = Sin
Adjacent side / Hypotenuse = Cos
Opposite side / Adjacent side = Tan

Cotangent is complementary tangent. So reciprocal of Cot is Tan.
Reciprocal of Secant is Cosine.
Reciprocal of Cosec is Sine.
C & C do not go together.
so also S & S.

In right angled triangle,
(1) Side opposite to 90 deg. is longest and it is called Hypotenuse. In short hyp.
In triangle ABC, if /_ B = 90 deg, then
AB sq + BC sq = AC sq
(2) Note letter B gets repeated. angle B is right angle.
(3) On R.H.S. B disappears and remaining letters get connected.