Kewal

Most popular questions and responses by Kewal
1. Trigonometry

If A + B + C = 180°, Prove that Cos²A + Cos²B + Cos²C = 1-2cosAcosBcosC

2. Trigonometry

Prove that cos(A+B) + sin(A-B) = 2sin(45°+A)cos(45°+B)

3. Trigonometry

If sinA + sinB = a and cosA + cosB = b, find the value of tanA-B/2

4. Trigonometry

Prove that 1-cosA+cosB-cos(A+B)/1+cosA-cosB-cos(A+B) = tanA/2cotA/2

5. Trigonometry

Prove that sin(A-B)/cosAcosB + sin(B-C)/cosBcosC + sin(C-A)/cosCcosA = 0

6. Trigonometry

IfA=340°, prove that 2sinA/2 = -(v1+sinA) + (v1-sinA)

7. Trigonometry

Prove that cos(A+B)cosC - cos(B+C)cosA = sinBsin(C-A)

8. Trigonometry

cos²a + cos²(a+120°) + cos(a-120°) = 3/2

9. Trig

sinAsin2A+sin3Asin6A+sin4Asin13A/sinAcos2A+sin3Acos6A+sin4Acos13A = tan9A

10. Trigonometry

If A + B + C = 180° prove that Sin2A + sin2B – sin2C = 4cosAcosBsinC

11. Trig

Prove that 1 + tanAtanA/2 = tanAcotA/2 -1 = secA

12. Trigonometry

cos2Acos2B + sin²(A-B) - sin²(A+B) = cos(2A+2B)

13. Trigonometry

If A + B + C = 180°, Prove that Cos²A + Cos²B - Cos²C = 1 – 2sinAsinBcosC

14. C++

Write a function that takes an int argument and doubles it. The function does not return a value.

15. Physics

A hemispherical bowl of radius R is rotated about its axis of symmetry which is kept vertical. A small block is kept in the bowl at a position where the radius makes an angle Θ with the vertical. The block rotates with the bowl without any slipping. The

16. Trigonometry

Prove that sin3A+sin2A-sinA = 4sinAcosA/2cos3A/2

17. Trigonometry

Prove that sin²A-sin²B/sinAcosA-sinBcosB = tan(A+B)

18. Trigonometry

Solve the equations for value of x tan mx + cot nx = 0

19. Maths

How many numbers less than 10000 can be formed by using digits 1,2,3,0,4,5,6,7 ?

20. Trigonometry

Prove that (tan4A + tan2A)(1-tan²3Atan²A) = 2tan3Asec²A

21. Trigonometry

Prove that tan2A = (sec2A+1)√sec²A-1

22. Trigonometry

If A + B + C = 180°, Prove that Sin² (A/2) + sin² (B/2) + sin²(C/2) = 1 – 2sin (A/2) sin (B/2) sin(C/2)

23. Trigonometry

If A + B + C = 180° prove that cos2A + cos2B – cos2C = -1 -4cosAcosBcosC

24. Trigonometry

If cospΘ + cosqΘ = o. prove that the different values of Θ form two arithmetical progressions in which the common differences are 2π/p+q and 2π/p-q respectively.

25. Trigonometry

Prove that sin(n+1)Asin(n-1)A + cos(n+1)Acos(n-1)A = cos2A

26. Trigonometry

If A + B + C = 180°, Prove that Sin² (A/2) + sin² (B/2) - sin²(C/2) = 1 – 2cos (A/2) cos (B/2) sin(C/2)

27. Straight Lines

From a given point (h,k) perpendiculars are drawn to the axis whose inclination is w and their feet are joined.Prove that the length of the perpendicular drawn from(h,k) upon this line is hksin²w/√(h² + k² + 2khcosw) and that its equation is hx - ky =

28. Straight Lines

Find the equation to and the length of the perpendicular drawn from the point(1,1) upon the straight line 3x + 4y + 5 = 0. The angle between the axis being 120°.

29. Straight Lines

The axes being inclined at an angle of 30°, find the equation to the straight line which passes through the point(-2,3) and is perpendicular to the straight line y + 3x = 6

30. Straight Lines

From each corner of a parallelogram a perpendicular is drawn upon the diagonal which does not pass through that corner and these are produced to form another parallelogram, show that its diagonals are perpendicular to the sides of the first parallelogram

31. Straight Lines

If y = xtan(11π/24) and y = xtan(19π/24) represents two straight lines at right angles, prove that the angle between the axis is π/4.

32. Binomial Theoram

If A be the sum of the odd terms and B the sum of the even terms in the expansion of (x+a)ⁿ. Prove that A² - B² = (x²-a²)ⁿ.

33. Straight Lines

Find the length of the perpendicular drawn from the point(4,-3) upon the straight line 6x + 3y - 10 = 0. The angle between the axes being 60°.

34. Straight Lines

With oblique coordinates find the tangent of the angle between the straight lines y = mx + c my + x = d

35. Trig

IfA=340°, prove that 2cosA/2 = -(v1+sinA) - (v1-sinA)

36. Trigonometry

Find all the angles between 0° and 90° which satisfy the equation sec²Θcosec²Θ + 2cosec²Θ = 8

37. Straight Lines

The coordinates of a point P referred to axis meeting at an angle w are (h,k). Prove that the length of the straight line joining the feet of the perpendiculars from P upon the axes is sinw√(h² + k² 2khcosw)

38. Physics

A turn of radius 20m is banked for the vehicles going at a speed of 36km/h. If the coefficient of static friction between road and the tyre is 0.4, what are the possible speeds of a vehicle so that it neither slips down nor skids up ?

39. Trigonometry

Solve the equations secΘ - 1 = (√2 - 1)tanΘ

40. Trigonometry

Prove that cos(-A+B+C) + cos(A-B+C) + cos(A+B-C) + cos(A+B+C) = 4cosAcosBcosC

41. Binomial Theoram

Show that the coefficient of the middle term of(1+x)power2n is equal to the sum of the coefficients of the two middle terms of (1+x)power2n-1.

42. Straight Lines

Find the equation to the sides and diagonals of a regular hexagon, two of its sides, which meet in a corner, being the axis of coordinates.

43. Straight Lines

Prove that the equation to a straight line which passes through the point (h,k) and is perpendicular to the axis of x is x + ycosΘ = h + kcosΘ

44. Trigonometry

Prove that sec8A-1/sec4A-1 = tan8A/tan2A

45. Trigonometry

Solve the equation tan²3Θ = cot²a

46. Trigonometry

Solve the equation cotΘ-abtanΘ = a-b Answer-tanΘ=1/a or -1/b

47. Trigonometry

Prove that cos(A+B+C)+cos(-A+B+C)+cos(A-B+C)+cos(A+B-C)/sin(A+B+C)+sin(-A+B+C)-sin(A-B+C)+sin(A+B-C) = cotB

48. Trigonometry

Prove that sin(n+1)A-sin(n-1)A/cos(n+1)A+2cosnA+cos(n-1)A = tanA/2

49. Trigonometry

Simplify sin{A + (n+1/2)B} + sin{A+(n+1/2)}

50. Trigonometry

Prove that sin(n+1)Asin(n+2)A + cos(n+1)Acos(n+2)A = cosA

51. Trigonometry

Solve the equation tan²3Θ = cot²a