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
tejas sanjay akole Grade: 12
        

 


to prove


(r=1 to r=7)∑tan2 rπ/16=35

7 years ago

Answers : (1)

Askiitians Expert Bharath-IITD
23 Points
										


ANS:


Let,


a=∏/16


tan7a=cota             since (∏/2-7∏/16=∏/16)


similarly we get,


tan6a=cot2a


tan5a=cot3a


and 4a =∏/4  tan4a=1


therefore given expression reduces to,


tan^2a+cot^2a+tan^2(2a)+cot^2(2a)+tan^2(3a)+cot^2(3a)+1


 


tan^2a+cot^2a=


=sin^4a+cos^4a/sin^2acos^2a


=((sin^2a+cos^2a)^2 – 2sin^2acos^2a)/ sin^2acos^2a


=(1– 2sin^2acos^2a) / sin^2acos^2a


=1/ sin^2acos^2a -2


=(4/4 sin^2acos^2a )-2


=4/sin^2(2a) -2


In the same way simplifying other sums we get,


4(1/sin^2(2a)+1/sin^2(4a)+1/sin^2(6a))-5


1/sin^2(4a)=2


=4(1/sin^2(2a)+1/sin^2(6a))+3


=8(1/(1-cos4a)+1/(1-cos12a))+3


[4a=∏/4  and  12a =3∏/4]


this gives


=32+3


=35


7 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies
  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: Rs. 15,900
  • View Details
Get extra Rs. 3,180 off
USE CODE: CART20
Get extra Rs. 127 off
USE CODE: CART20

Ask Experts

Have any Question? Ask Experts

Post Question

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