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ISC Class XI Notes 2024 : Physics Vector (Mathematical Tools))

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Kolabari Tutorial Physics XI Comprehensive Study material Mathematical Tools for Physics Quadratic Equation An equation of second degree is called a quadratic equation. It is of the form :- ax2 + bx + c =0 The roots of a quadratic equation are X = Binomial Theorem If n is any integer, positive or negative or a fraction and x is any real number, then ( 1+x)n = 1 + nx + x2 + .. . If IxI <<1 , then (1+x)n = 1+ nx. Mensuration 1. Area of a circle = r2 = D2/4 2. Surface area of a sphere = 4 r2 = D2 4. Surface area of a cylinder = 2 r(r+l) 6. Curved surface area of a cone = rl 8. Surface area of a cube = 6 x (side)2 3. Volume of a sphere = (4/3) r3 5. Volume of a cylinder = r2 l 7. Volume of a cone = (1/3) r2h 9. Volume of a cube = (side)3 Fundamental Trigonometric relations Cosec = 2 Sec = 2 Cot = 2 2 = 2 Sin + Cos =1 1+ tan =Sec Sin(A+B) = SinACosB + CosASinB Cos (A + B) = CosACosB SinASinB Tan = 2 1+ Cot = Cosec Sin (A B) = SinACosB CosASinB Cos (A B) = CosACosB + SinASinB Tan (A B) = Sin 2A = 2SinACosA Sin (A+B) + Sin(A-B) = 2 SinACosB Cos 2A = 2Cos2A 1=1- 2Sin2A = Cos2A Sin2A Sin C + Sin D = 2 Sin Cos Cos(A+B) + Cos (A-B) = 2CosACosB Cos C + Cos D = 2Cos x - - + - sinx -sin cos cos cosx cos sin -sin tanx - tan cot -cot + - sin -sin -cos -cos -cos -sin -tan tan cot Cos + 2 - 2 + -cos sin -cot -sin cos -tan sin cos tan Logarithms Logamn = Logam + Logan Logam = Logbm x Logab Logaa = 1 Loga = Logam - Logan n Logaa = n ax = Logamn = nLogam Loga1 = 0 Approximate Values If angle ( ) is very small then i.e. 0, then Sin ; Cos 1 and Tan Differential Calculus Kolabari Tutorial [Near: Bharat Gas Godown Devidanga, champasari, Siliguri. Contact : 8116600677] www.kolabaritutorial.weebly.com Page 1

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Additional Info : Vector; Differentiation, Integration
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