How to multiply numbers near to 100

consider two numbers near to 100

e.g 97 and 98

Subtract  both these from 100

100-97 = 3
100 -98 = 2

Now add of them (3+2) = 5
Remove this from 100 i.e. 100-5 = 95

Now mutliply them 3 x 2 = 06

so the result will be 95 and append 06 => 9506

Let us take another example

92 x 97
100 -92 = 8
100-97 = 3

8+3 = 11, remove this from 100 i.e. 89
now multiply 8 x 3 = 24
so the answer is 8924

Try the below

1. 94 x 96
2. 99 x 91

Table 9 with hands

Instead of memorizing the table 9, use your hands to multiply

Face your palms as shown above

If you have to mutliply 9 x 3, fold the 3rd finger

if you check now, there will be two fingers on left side and 7 fingers on right side

keep the left value in tens and right value in ones i.e. 2 7

Let us take one more example 9 x 7, now fold the 7th finger, you will have now 6 fingers on left side and 3 fingers on right side so the value will be 6 3

Simple Trigonometry

Remember the above image and we can derive the below values easily

sin(0) = cos(90) = sin(180) = cos(270) =  sin(360) = cos(-90) = 0
cos(0) = sin(90) = 1
cos(180) = sin(270) = -1

sin(A + B) = sin A cos B + cos A sin B
cos(A + B) = cos A cos B − sin A sin B

sin(A − B) = sin A cos B − cos A sin B
cos(A − B) = cos A cos B + sin A sin B