MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12th Pass
        The equations kcosx - 3sinx=k+1 is solvable only if k belongs to the interval?

7 years ago

Answers : (1)

Praneetha reddy
36 Points
							

k(cos x) - 3(sin x) = k + 1
k(cos x) - (k + 1) = 3(sin x)
[k(cos x) - (k + 1)]^2 = [3(sin x)]^2
k^2cos^2x - 2k(k + 1)(cos x) + (k + 1)^2 = 9sin^2x
k^2cos^2x - (2k^2 + 2k)(cos x) + (k + 1)^2 = 9(1 - cos^2x)
(k^2 + 9)cos^2x - (2k^2 + 2k)(cos x) + (k^2 + 2k - 8) = 0

Here we have a quadratic equation in terms of (cos x).
This equation is only solvable when the determinant b² - 4ac greater than or equal to 0, otherwise the solution will be complex.

b² - 4ac greater than or equal to 0
[-(2k^2 + 2k)]^2 - 4(k^2 + 9)(k^2 + 2k - 8) greater than or equal to 0
(4k^4 + 8k^3 + 4k^2) - (4k^4 + 8k^3 + 4k^2 + 72k - 288) greater than or equal to 0
-72k + 288 greater than or equal to 0
72k less than or equal to 288
k less than or equal to 4

i.e. -infinity<k<4

= k belongs to (-infinity, 4]

7 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 31 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details