Question

I am in class 8 :
What are the formulas [ not in syllabus just curious ] :

sin2A
cos2A
tan(A+B)
sin(A+B)
cos(A+B)
What is factorial of a number ?
What is binomial theorem ? [ please explain in simple language only please please ]

Answer 1

2sinAcosA
$cos {}^{2} a - 1$
$tana + tanb \div 1 - tanatanb$
SinAcosB+cosAsinB

CosAcosB-sinAsinB

$bianomial \: theorem \: = ac {}^{2} = ab {}^{2} + bc {}^{2}$

Answer 2

Class 8 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!  

I learnt these in class 10 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!  

$\boxed{\bf{Formulas}}$  

sin 2A = 2 sin A × cos A  

cos 2A = 2 cos² A - 1  

tan ( A + B ) = ( tan A + tan B ) / ( 1 - tan A tan B )  

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

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

====================================================  

FACTORIAL  

Factorial ??? I learnt in class 6 XD  

Factorial of a number is the multiplication of all positive integers before the number ...  

$\bf{Examples}$  

5! = 1 × 2 × 3 × 4 × 5  

= 120  

Remember 0 ! = 1  

Also remember : n = n! / ( n - 1 )!  

This means that : -1! does not exist  

n! / n = ( n - 1 )!  

- 1 ! = ( 0 ! ) / 0  

= 1/0 = undefined  

Negative integer's factorials do not exist .  

$\boxed{\bf{BINOMIAL\:THEOREM}}$  

Binomial theorem helps to multiply and expand an expression easily !

$(a+b)^n=^nC_{0}a^n+^nC_{1}a^{n-1}b+..................^nC_{n-1}ab^{n-1} +^nC_{n}b^n$

This is the formula of the Theorem !

$^nC_{r}=\frac{n!}{(n-r)!\timesr!}$

Very hard ? Making it easy wait |!!!!!!

$\bf{EXAMLES}$

• $(a+b)^3=a^3+3a^2b+3ab^2+b^3$
• $(a+b)^5=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5$
• $(a+b)^8=a^8+8a^7b+28a^6b^2+56a^5b^3+70a^4b^4+56a^3b^5+28a^2b^6+8ab^7+b^8$

Hope it helps :-)

If you don't understand ask me !

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