Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
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

f sides of a tringle a,b,c are in AP then prove that : COSA.COTA/2, COSB.COTB/2, COSC.COTC/2 ARE IN AP. 37 minutes ago Answers : (1)

 
f sides of a tringle  a,b,c are in AP then prove that :
COSA.COTA/2, COSB.COTB/2, COSC.COTC/2 ARE IN AP. 
37 minutes ago
 

Answers : (1)

Grade:12th pass

1 Answers

Vikas TU
14149 Points
4 years ago
Dear Student,
 
cot A/2= (cos A/2)/(sin A/2) = 2 cos^2A/2/sin A = (cos A+1)/ Sin A
Therfore,
Visulaizing 1st term = cos^2 A/sin A + cos A/sin A = (1-sin ^2A)/sin A+ cos A/sin A
= (1+ cos A)/sin A - sin A
so ,as sin A sin B and sin C are in AP we need to show that
(1+cos A)/Sin A, (1+ cos B)/sin B, (1+ cos C)/sin C are in AP
1+ cos A = 1+ (b^2+c^2-a^2)/2bc
= (2bc+b^2+c^2-a^2)/2bc
so (1+cos A)/sin A = (2bc +( b^2+c^2-a^2)/2abc k
as sin A/ a= sin B/b = sin C/c = k
(1+Cos C)/sin C = (2ab+(b^+a^2-c^2)/2abck
so, (1+cos A)/Sin A, (1+ cos B)/sin B, (1+ cos C)/sin C are in AP
Now,as sin A, sin B sin C are in AP and also (1+cos A)/Sin A, (1+ cos B)/sin B, (1+ cos C)/sin C are in AP, so cosA.cotA/2,cosB.cotB/2, cosC.cotC/2 are in AP (Hence proved).
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free