Integration Formulas...

Arithmatic Progression...

a_n=a+(n-1)d

d=T_(n+1)-T_n

S_n=n/2*(2a+(n-1)d)

T_n=S_(n+1)-S_n

Basic Units conversions :-

Perimeter of Basic Geometrical figures...

• square=4a
• Rectangle=2*(l+b)
• circle=2*Π*r

Volume Formula's of some Geometrical figures...

cube=a³

Rectangular prism=l*b*h

Cylinder=Πr²h

cone=1/3*Π*r²h

sphere=4/3*Π*r³

Hemisphere=2/3*Π*r³

Sum/Difference Identities:-

• sin(x+y)=sinx.cosy+cosx.siny   

• sin(x-y)=sinx.cosy-cosx.siny

• cos(x+y)=cosx.cosy-sinx.siny

•  cos(x-y)=cosx.cosy+sinx.siny

→sinθ=1/cosecθ

→cosθ=1/secθ

→tanθ=sinθ/cosθ

→cotθ=cosθ/sinθ

→secθ=1/cosθ

→cosecθ=1/sinθ

Pythagorean Identities:-

• sin²θ+cos²θ=1
• tan²θ+1=sec²θ
• cot²θ+1=cosec²θ

• tanx.cotx=1
• secx.cosx=1
• sinx.cosecx=1

→sinθ=perpendicular/Hypotenuse

→cosθ=Base/Hypotenuse

→tanθ=Perpendicular/Base

→cotθ=Base/Perpendicular

→secθ=Hypotenuse/Base
→cosecθ=Hypotenuse/Perpendicular

Area's Related to Geometrical Figures :-

→Square= a²

→Rectangle=l×b

→Triangle= ½×base×height

→parallelogram= base×height

→circle=Π×r²

→Cylinder= °curved surface area=2Πrh

                  °Total surface area  =2Πrh + 2Πr²

→Rectangular solid= 2(lb+bh+hl)

→cone = Πr²+Πrl , where l=√(r² + h²)

→sphere = 4Πr²

Factoring Equations:-

• (a+b)²= a²+b²+2ab
• (a-b)²= a²+b²-2ab
• a²-b²= (a+b)(a-b)
• a³+b³= (a+b)(a²+b²-ab)
• a³-b³= (a-b)(a²+b²+ab)
• (a+b)³= a³+b³+3ab(a+b)
• (a-b)³= a³-b³-3ab(a-b)
• a³+b³+c³-3a b c=(a+b+c)(a²+b²+c²-ab-b c-ca)
• If a+b+c=0 then a³+b³+c³=3a b c