badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
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: 11

                        

The number of solutions of the equation cos x=sin^2x,x belongs to 0,6 pi

4 months ago

Answers : (1)

Aditya Gupta
2069 Points
							
dear student, first write the given eqn as C^2+C – 1=0 where C= cosx.
now note that the period of the function f(x)= C^2+C – 1 is 2pi. Hence, we only need to find the no of solns in (0, 2pi), and simply triple that to find the no of solns in (0, 6pi).
Now on setting C^2+C – 1=0, we get C= (– 1 ± sqrt5)/2.
as (– 1 – sqrt5)/2 is less than – 1, we reject it coz C lies in [-1,1].
so we get only C= (– 1+sqrt5)/2. 
Now, if you draw the graph of y= cosx and y= (– 1+sqrt5)/2, they clearly intersect at only 2 points in [0, 2pi].
Hence, total no of solns in [0, 6pi] is 3*2
6
KINDLY APPROVE :))
4 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

  • 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