Inverse trigonometry formulae play a vital role in solving a variety of mathematical and real-world problems. These formulas, such as arcsin, arccos, and arctan, allow us to find the angles associated with specific trigonometric ratios. They are essential tools for trigonometric calculations involving triangles, physics, engineering, and more. Inverse Trigonometric Formulae Class 12 1. should … Read more
Chapter 2 Miscellaneous(Sets) Class 11 Question 1: The relation f is defined by The relation g is defined by Show that f is a function and g is not a function. Solution: The given relation f is defined as: It is seen that for 0 ≤ x < 3, f(x) = x2 and for 3 < x ≤ 10, f(x) = 3x Also, at x = 3 f(x) = 32 = 9 … Read more
EXERCISE 2.3 (Class 11) 1. Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range. (i) {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)} (ii) {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)} (iii) {(1, … Read more
EXERCISE 2.2 (Class 11) 1. Let A = {1, 2, 3, … , 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range. Solution: The relation R from A to A is given as: R = {(x, y): 3x – y = 0, … Read more
EXERCISE 2.1(Class 11) 1. If , find the values of x and y. Solution: Given, As the ordered pairs are equal, the corresponding elements should also be equal. Thus, x/3 + 1 = 5/3 and y – 2/3 = 1/3 Solving, x + 3 = 5 and 3y – 2 = 1 [Taking L.C.M. and … Read more
Chapter 2: Miscellaneous Exercise Find the value of the following:(Class 12 ncert solution math chapter 2 Miscellaneous) Question 1: Find the value of . Solution: Question 2: Find the value of . Solution: Question 3: Prove that . Solution: Let Then, Therefore, Thus, Question 4: Prove that . Solution: Let Then, Therefore, Now, let Then, … Read more
EXERCISE 2.2 Prove the following:(Class 12 ncert solution math exercise 2.2) Question 1: Prove . Solution: Let Hence, Now, =L H S Question 2: Prove . Solution: Let Hence, Now, Question 3: Prove . Solution: Since we know that Now, Question 4:Prove . Solution: Since we know that Now, Question 5: … Read more
Embarking on the realm of inverse trigonometry in Class 12 NCERT solution Math Exercise 2.1 serve as an invaluable resource for students. This section dives into the intricate world of inverse trigonometric functions, unraveling their properties, and elucidating the nuances of solving problems related to them. The solutions provide a meticulous guide, offering step-by-step explanations … Read more