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: 
        
if α and β are acute angles and cos2α=3cos2β-1/3-cos2β , show that tanα=√2 tanβ
6 years ago

Answers : (1)

Jitender Singh
IIT Delhi
askIITians Faculty
158 Points 
							Ans:Hello student, please find answer to your question
tan\alpha = \sqrt{2}tan\beta
cos2\alpha = \frac{1-tan^{2}\alpha }{1+tan^{2}\alpha }
RHS = cos2\alpha = \frac{1-(\sqrt{2}tan\beta )^{2} }{1+(\sqrt{2}tan\beta )^{2}}
RHS = cos2\alpha = \frac{1-2tan^{2}\beta }{1+2tan^{2}\beta }
LHS = \frac{3cos2\beta -1}{3-cos2\beta }
LHS = \frac{3.\frac{1-tan^{2}\beta }{1+tan^{2}\beta } -1}{3-\frac{1-tan^{2}\beta }{1+tan^{2}\beta } }
LHS = \frac{3-3tan^{2}\beta-1-tan^{2}\beta }{3+3tan^{2}\beta-1+tan^{2}\beta }
LHS = \frac{2-4tan^{2}\beta}{2+4tan^{2}\beta}
LHS = \frac{1-2tan^{2}\beta}{1+2tan^{2}\beta}
Hence, proved
4 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Other Related Questions on Trigonometry

If CosA*CosB*CosC = ((root3)-1)/8 SinA*SinB*SinC = (3+(root3))/8 then values of A, B, C? Answer & Earn Cool Goodies
ABC is an isosceles right angle triangle with AB=BC =1.If P is a point on AC then... Answer & Earn Cool Goodies
Please answer the question nd thanks in advance.the question number is 14 and has 3 parts .plese...
If 3Sinx + 12Siny + 4Cosx + 5Cosy = 18, then value of tan(x+y) =
If Sinx+cosx=√2tanx then what is the value of tanx and how can we solve this problem
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