MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
aritra nandy Grade: 10
        (1+tan 1)(1+tan 2)(1+tan 3)+(1+tan 4)..................(1+tan 45)=2^n(two to the power n)

find the value of n
6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

(1+tan1)(1+tan2)(1+tan3) .................(1+tan45) = 2n


                                                                                        (1+tan45 = 1+1=2)


(1+tan1)(1+tan2) ........................(1+tan44) = 2n-1


now make pairing such that sum of angles is 45...


[(1+tan1)(1+tan44)][(1+tan2)(1+tan43) ...................[(1+tan22)(1+tan23)] = 2n-1 


 


now take any of pair separately ,let its value be k then


k=(1+tan1)(1+tan44) = 1 + tan44 + tan1 + tan1tan44         .................1


tan45 = tan(44+1) = (tan44+tan1)/(1-tan1tan44)          .......................2


from eq2 put  ( tan1+tan44) in eq 1


k=1 + tan45 = 2


now there will be 22 pairs  so the value of expression is


k.k.k.k............22terms = 2n-1


k22 = 2n-1


222 = 2n-1


n = 23 ans


approve my ans if u like


 

6 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 15,000 off
USE CODE: asksch70
Get extra R 600 off
USE CODE: asksch70

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details