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
        
if alpha and beta are the roots of the equation 3cosx+4sinx=5 then cot(alpha+beta) equals
4 months ago

Answers : (3)

Arun
24735 Points
							
3cosx + 4sinx = Asin(x + Ф)
 
Multiply and divide with = 5 in LHS
e.g., (3cosx + 4sinx)/5 = Asin(x + Ф)
⇒5(3/5.cosx + 4/5.sinx) = Asin(x + Ф)
 
Let cosФ= 3/5 then, sinФ = 4/5
Now, tanФ = sinФ/cosФ = 4/3
⇒ Ф = tan⁻¹(4/3) ----(1)
 
And 5(3/5.cosx + 4/5.sinx)= 5(sinФ.cosx + cosФ.sinx) = Asin(x + Ф)
⇒ 5sin(x + Ф) = Asin(x + Ф)
From equation (1),
⇒ 5sin(x + tan⁻¹(4/3)) = Asin(x + Ф)
Compare both sides,
A = 5 and Ф = tan⁻¹(4/3)
4 months ago
Saurabh Koranglekar
askIITians Faculty
8373 Points
							Dear student

The simplification is

Sin ( x + 37 ) = 1= sin ( 90+ 2n*pi)

You can solve accordingly by evaluating alpha and beta

Regards
4 months ago
Aditya Gupta
2016 Points
							
note that aruns soln doesnt answer the ques.
we use the standard formulas:
cosx= (1 – t^2)/(1+t^2) and sinx= 2t/(1+t^2) where t= tan(x/2).
so eqn becomes
3(1 – t^2)+4(2t)= 5(1+t^2)
or 8t^2 – 8t + 2= 0 
or 4t^2 – 4t + 1= 0
or (2t – 1)^2= 0
or t= tan(x/2)= ½ so that tan(p)= tan(q)= ½ where p= alpha/2 and q= beta/2.
cot(alpha+beta)= 1/tan(alpha+beta)= 1/tan(2p + 2q)= (1 – tan2p*tan2q)/(tan2p + tan2q)
now, tan2p= 2tanp/(1 – tan^2p)= 4/3. similarly tan2q= 4/3
hence, cot(alpha+beta)= (1 – tan2p*tan2q)/(tan2p + tan2q)= – 7/24
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