0

Guest

Courses New

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
25750 Points
6 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 ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More