Properties of Inverse Trigonometric Functions – Problems Property I: (i) sin¯¹ (sin θ) = θ for all θ ϵ [-π / 2, π / 2] (ii) cos¯¹ (cos θ) = θ for all θ ϵ [0, π] (iii) tan¯¹ (tan θ) = θ for all θ ϵ [-π / 2, π / 2] (iv) cosec¯¹ Read more about Properties of Inverse Trigonometric Functions – Problems[…]
Trigonometric Functions and Equations – Transformation i) sin (A + B) + sin (A – B) = 2 sin A cos B, ii) sin (A + B) – sin (A – B) = 2 cos A sin B, iii) cos (A + B) + cos (A – B) = 2 cos A cos B, iv) Read more about Trigonometric Functions and Equations – Transformation[…]
Trigonometrical or Polar representation of Complex Numbers Let z = x + iy is a complex number which is denoted by a point P (x, y) in a complex plane, then OP = |z| and ∠POX = θ = arg (Z). In ΔPOM, , , Then x = |z| cosθ and θ. . . Then Read more about Trigonometrical or Polar representation of Complex Numbers[…]
Complex Numbers – Position of a Point with respect to Circle Position of a Point with respect to Circle: Let the general equation of the circle is . Whose center z₀ and radius a. there are following position with respect to circle are given below. a) If the point (z₀) lies inside the circle, then Read more about Complex Numbers – Position of a Point with respect to Circle[…]
Locus – Algorithm Definition of Locus: In geometry, a locus is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions. Equation to the Locus of a Point: The equation to the locus of a point is Read more about Locus – Algorithm[…]
Reciprocal Arguments and Inverse Sum Identities Reciprocal Arguments: (i) sin⁻¹ (1/x) = cosec⁻¹ x, ∀ x ϵ (-∞, -1] ∪ [1, ∞), (ii) cos⁻¹ (1/x) = sec⁻¹ x, ∀ x ϵ (-∞, -1] ∪ [1, ∞), (iii) . Inverse Sum Identities: (i) sin⁻¹ x + cos⁻¹ x = π/ 2, ∀ x ϵ [-1, 1], Read more about Reciprocal Arguments and Inverse Sum Identities[…]
Properties of Determinants – 1 Property 1: Let A = [aij] be a square matrix of order n then the sum of the product of elements of any row (columns) with their cofactors is always equal to |A| or det (A) i.e, and . Property 2: Let A = [aij] be a square matrix of Read more about Properties of Determinants – 1[…]
Trace of a Matrix Let A = [aij]mxn be a square matrix. Then, the sum of all diagonal elements of A is called the trace of A and is denoted by tr(A). Thus, . Properties of Trace of Matrix: Let A = [aij] and B = [bij] are two square matrix of order n then Read more about Trace of a Matrix[…]
Angle of Intersection of Two Curves The angle of intersection of two curves is the angle subtended between the tangents at their point of intersection. Let C₁ and C₂ be two curves having equations y = f(x) and y = g(x), respectively. Let PT₁ and PT₂ be tangents to the curves C₁ and C₂ at Read more about Angle of Intersection of Two Curves[…]
Some Important Integrals (i) . (ii) . (iii) . Example: is equal to ? Solution: Given, , Here, we can convert the integrand into some standard integrand of the form and then integrate. Let, , , (∵ ), , . Share Tweet View Email Print Follow