Mohd. Asad's Maths Worksheet PDF

# Maths Worksheet **Name:** Mohd. Asad **Class:** XII th ** Father's Name:** Saeed Khan **Date:** 28/06/21 **Subject:** Maths ## Questions 1. (ii) π/4 2. (iii) π/3 3. (iii) π/2 4. tan-1 3/4 5. (ii) 0 6. (iv) M=N 7. (ii) 5√2 8. (ii) 5π/6 9. (ii) 2xn 10. (iii) π/4 ## Question 11 2x( ½) + y(-1) =...

# Maths Worksheet **Name:** Mohd. Asad **Class:** XII th ** Father's Name:** Saeed Khan **Date:** 28/06/21 **Subject:** Maths ## Questions 1. (ii) π/4 2. (iii) π/3 3. (iii) π/2 4. tan-1 3/4 5. (ii) 0 6. (iv) M=N 7. (ii) 5√2 8. (ii) 5π/6 9. (ii) 2xn 10. (iii) π/4 ## Question 11 2x( ½) + y(-1) = 10 5 [2x] + [-y] = 10 5 [2x-3] = 10 (Matrices are equal) [3x+y] 5 (Corresponding elements are equal) 2x-y= 10 - (1) 3x+y = 5 - (2) Adding 1 & 2 (2x-y) + (3x+y) = 10 + 5 2x+3x-y+y = 15 5x = 15 x = 3 Putting value of x in eq. 1 2x - y = 10 2(3) - y = 10 6 - y = 10 y = -4 ## Question 12 tan-1 [cos x -sin x] cosx+sin x Dividing by cos x inside = tan-1 [cos x-sin x/cos x] cos x+sin x/cos x = tan-1 [cos x/cos x - sin x/cos x] cos x/cos x+ sin x/cos x = tan-1 [1- tan x] 1 + tan x = tan-1 [1-tan x] 1+tan x = tan-1 [tan π/4 - tan x] (tan π/4= 1) 1 + tan π/4.tan x = π - x 4 ## Question 14 sin [sin-1 ½ + cos-1 x] = 1 Putting sin π/2 = 1 sin [sin-1 ½ + cos-1 x] = sin π/2 Comparing angles sin-1 ½ + cos-1 x = π/2 Sin-1 ½ = sin π/2 Thus, we can write sin y 2 = π/2 = cos x ½ = 2 x = 1 5 Hence, x = 1/5 ## Question 15 Taking L.H.S gives A = [cos x - sin x] [sin x cos x] So A' = [cos x - sin x] [sin x cos x] A'A = [cos x - sin x] [cos x sin x] [sin x cos x] [ - sin x cos x] = [cos x.cos x + (-sin x). (- sin x)] [sin x. cos x + cos x.(- sin x)] = [cos² x + sin² x] [sin x cos x - cos x sin x] = [cos² x + sin² x + (-sin x)(cos x)] [sin x. sin x + cos x. cos x] = [cos² x + sin² x] [sin x cos x - sin x cos x] [sin x cos x - sin x cos x] [sin² x + cos² x] = [cos² x + sin² x] [0] [sin² x + cos² x] Using sin² θ + cos² θ = 1 [1] [0] [1] = 1 = R.H.S Hence L.H.S = R.H.S Hence proved. ## Question 13 (A+B)'= [-5 8 -2] [6 3 9] [-1 4 2] = [-5 6 1] [3 9 4] [-2 9 2] A+B' = [-1 5 -2] + [-4 1 1] [2 7 1] [1 2 3] [3 9 1] [-5 0 1] = [-5 6 -1] [3 9 4] [-2 9 2] Hence, proved (A+B)'=A'+B'