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:
        
The maximum value of the expression sinx +ncosx,when x can take any value is
7 months ago

Answers : (2)

Vikas TU
10430 Points
							
Dear student 
Sinx + nCosx 
Multiply and divide by [(coefficient of sinx)^2+(coefficient of cosx)^2]^1/2 i.e. in this condition
(n^2+1^2)^1/2
Now the equation transforms to
[sinx/(n^2+1^2)^1/2+ncosx/(n^2+12)^1/2]×(n^2+1^2)^1/2
Now consider a triangle with angle ø.
Let the perpendicular length be n and base be 1.
So hypotenuse is (n^2+1^2)^1/2
Therefore our equation transforms to
[cosøsinx+sinøcosx]×(n^2+1^2)^1/2
sin(ø+x)×(n^2+1^2)^1/2
As max value of sin(x+ø) is 1
So maximum value of  sin(ø+x)×(n^2+1^2) ^1/2 is (n^2+1^2)^1/2 which is the maximum value of our original equation.
So max value is [(coefficient of sinx)2+(coefficient of cosx)2]^1/2
7 months ago
Rajat
213 Points
							
f=sinx+ncosx
f'= cosx -nsinx=0 (for maximum )
So tanx = 1/n
So, sinx= 1/√(1+n^2)
sinx+ncosx=1/√(1+n^2)+n^2/√(1+n^2)
= √(1+n^2)
 
7 months 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

  • 18 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