Complex number and trigno

De Moivre's formula

If you ever find yourself trying to remember any one of those basic trigonometric formulas, the ideal starting point is the De Moivre's formula:

Above we have given you some examples of identities that can be easily derived using this formula. In fact, most trigonometric relations can be obtained from this formula after performing some basic algebra.

 

17 equations that changed the world.

Pythagoras Theorem

Pythagoras Theorem :- A theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

h² = P² + B²

Infinite Series : - Convergence and Divergence, Alternating Series, Liebnitz's test, Absolute Convergence and Conditional Convergence

Integration formula

Formula of Conic Section

1. Formula of circle

(x-h)² + (y-k)² = r²
Where C(h,k) is centre
P(x,y) is point on circle
And CP = r is radius of circle




2. Formula of parabola
       

 Directrix is called the fixed line.
Focus is the fixed point F.
Axis of parabola is a line through the focus and perpendicular to the directrix.

 

*  y² = 4ax

 * y² = -4ax

 

* x² = 4ay

* x² = -4ay







Latus rectum of a parabola is a line segment perpendicular to the axis of the parabola, through the focus and whose end points lie on the parabola.

Length of latus rectum = 4a

Question 16, Chapter 7, Class 12, Mathematics, NCRT ,CBSE

Solution 16.

A TEXT BOOK of MACHINE DESIGN by R.S Khurmi and J.K Gupta

Example 43 , Chapter 7, Class 12 , Mathematics, NCRT, CBSE

Example 43. Evaluate