## If cos y = x cos (a + y) with cos a ≠ ± 1 then prove that

Question: If , with , then prove that . Hence show that . ……..      [CBSC  2016] Solution: Given, Differentiating with respect to y on both sides, we get Differentiating both sides w.r.t. x, we get Some other question: Q 1: If , Prove that .    ……..[CBSC 2020] Solution: For solution click here … Read more

## Find the value of dy/dx at θ = pi/4, if x = aeθ(sin θ – cos θ)

Question: Find the value of at , if and .          ……..   [CBSC 2008, 2014] Solution: Given, and Taking, Differentiating with respect to θ, we get Again taking, Differentiating with respect to θ, we get Some other question: Q 1: If , Prove that .    ……..[CBSC 2020] Solution : For solution … Read more

## If tan inverse y/x = log root x^2 + y^2, then prove that

Question: If , Prove that .    ……..[CBSC 2020] Solution: Given, Differentiating with respect to x, we have, Some other question: Q 1: If , then prove that Q 2: Find the value of at , if and .          ……..   [CBSC 2008, 2014]

## If y^x = e^(y-x), then prove that dy/dx = (1 + logy)^2/log y

Question: If , then prove that Solution: Given, Taking logrithm both sides, we get log Differentiating both sides with respect to y, we get Some other question Q 1 :If tan inverse y/x = log root x^2 + y^2, then prove that Q 2: Find the value of at , if and .      … Read more

## Class 10 Case study Chapter 8 introduction to Trigonometry

Class 10 Case study Chapter 8 introduction to Trigonometry Case Study:1     An electrician wanted to repair a street lamp at a height of 15 feet. He places his ladder such that its foot is 8 feet from the foot of the lamp post as shown in the figure below: (A) Find the value … Read more

## Class 10 Case study of Chapter 7 coordinate geometry

Class 10 Case study of Chapter 7 coordinate geometry  Case study:1                 To conduct Annual day activities, in a rectangular shaped school ground PQRS, lines have been drawn with chalk powder at a distance of 1 m each.  10 banners have been placed at a distance of 10 … Read more

## If α and β are the zeros of the quadratic polynomial

Question:             If α and β are the zeros of the quadratic polynomial f(x) = ax² + bx + c, then evaluate: (i)  (ii)  (iii) (iv) (v)  (vi) Solution: Since α and β are the zeros of the quadratic polynomial f(x) = ax² + bx + c and (i) We … Read more

## If we add 1 to the numerator and subtract 1 from the

Question:1                    If we add 1 to the numerator and subtract 1 from the denominator, a fraction becomes 1. It also becomes 1/2 if we add 1 to the denominator. What is the fraction. Solution: Let the fraction Then, according to the first condition, we have ……..(i) … Read more

## Find the zeros of the quadratic polynomial x² + 7x + 12

Question:1               Find the zeros of the quadratic polynomial x² + 7x + 12, and verify the relation between the zeros and its coefficients. Solution: We  have, f(x) = x² + 7x + 12 f(x) = x² + 7x + 12 ⇒ f(x) = x² + 4x + 3x … Read more

## Class 10 Case based problem of Chapter 6 Triangles 2

Class 10 Case based problem of Chapter 6 Triangles 1 Class 10 Case based problem of Chapter 6 Triangles 2  Case study:1 While browsing through the catalogue of wooden shelves. Ravi came across this beautiful triangular shaped shelf. A shelf DE parallel to the base BC could be used for displaying small plants and showpieces … Read more