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

In any triangle ABC,Prove that a(cosC-cosB)=2(b-c)cos²A/2

In any triangle ABC,Prove that a(cosC-cosB)=2(b-c)cos²A/2

Grade:11

1 Answers

Arun
25763 Points
4 years ago
(A/2)/ (cosC-cosB)2(A/2)/ 2 sin((B+C)/2) cos(B-C/2)=cos2(A/2)/ 2 sin((B+C)/2) cos(B-C/2)= 2 cos2(A/2)/ Cos(90 – (B+C)/2) cos(B-C/2)=2 cos2(A/2)/ Cos(A/2) cos(B-C/2)= cos2a/ 2(b-c) = cos^2(A/2)/ (cosC-cosB)lhs = a / 2 (b – c )Now use sine rulea/ sinA = b/ sinB = c/ sinC = kSo, lhs = a / 2 (b – c )= sinA / 2(sinB -sinC)=SinA /2* 2 cos(B+C/2) cos (B-C/2)= sinA / 4 cos (pi/2 – A/2) cos (B-C/2)=2 sin(A/2) cos (A/2) / 4 sin(A/2) cos (B-C/2)= cos (A/2) / cos(B-C/2)=cos

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