MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

⇐ BackProceed to Checkout ⇒
There are no items in this cart.
Continue Shopping
Menu
Grade: 12 
        
Let α and β be non–zero real numbers such that 2(cosβ – cosα) + cosα cosβ = 1. Then which of the following is/are true?
 
one year ago

Answers : (1)

Umang Kumar
15 Points 
							
2(cosb-cosa)+cosa.cosb=1
2cosb-2cosa+cosa.cosb=1
cosb(2+cosa)-(2cosa+1)=0
cos\beta =\frac{2cos\alpha +1}{2+cos\alpha }
Now converting cos\beta =\frac{1-tan^{2}\frac{\beta }{2}}{1+tan^{2}\frac{\beta }{2}}
cos\alpha =\frac{1-tan^{2}\frac{\alpha }{2}}{1+tan^{2}\frac{\alpha }{2}}
now equating cosa and cosb in
cos\beta =\frac{2cos\alpha +1}{2+cos\alpha }
we get
\frac{1-tan^{2}\frac{\beta }{2}}{1+tan^{2}\frac{\beta }{2}}=\frac{3-tan^{2}\frac{\alpha }{2}}{3+tan^{2}\frac{\alpha }{2}}
After applying Componendo and dividendo method each side we get:
\frac{2}{-2tan^{2}\frac{\beta }{2}}=\frac{6}{-2tan^{2}\frac{\alpha }{2}}
After solving this we get:
\frac{1}{tan^{2}\frac{\beta }{2}}=\frac{3}{tan^{2}\frac{\alpha }{2}}
After cross multiplying we get:
tan^{2\frac{\alpha }{2}}=3tan^{2\frac{\beta }{2}}
Square root both side:
tan\frac{\alpha }{2}=\pm \sqrt{3}tan\frac{\beta }{2}
hence the answers are:-
1.tan\frac{\alpha }{2}+\sqrt{3}tan\frac{\beta }{2}=0
2.tan\frac{\alpha }{2}-\sqrt{3}tan\frac{\beta }{2}=0
 
one year ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Other Related Questions on Trigonometry

please answer me as soon as possible as given in attachment Answer & Earn Cool Goodies
Question no 21 and 22.. can anybody solve the anawer step by step and post it as soon as... Answer & Earn Cool Goodies
Find the principal solution of sin theta = sin2 theta
a pendulum swings at angle 42 degree in describing an arc of lenght 55 cm . the lenght of the...
Please can you help me with these problems simplify problem1 (sinα +sinβ) /( cosα −cosβ)
View all Questions »


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