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if A+B+C=pi then prove cosA/2+cosB/2+cosC/2=4cosB+C/4×cosC+A/4×cosA+B/4

if A+B+C=pi then prove cosA/2+cosB/2+cosC/2=4cosB+C/4×cosC+A/4×cosA+B/4
 

Grade:11

2 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
8 years ago
Hii

replace cosC/2 with cos(pi – A-B)/2 and then use the simplification and you will get the answer after a bit of rearrangement
HARINI
34 Points
6 years ago
A+B+C=PIE
COSA/2+cosb/2+cosc/2
  • cosa/2+2cosb+c/4 +2cosb-c/4
  • a+b+c=pie =cosa/2=cos(pie/2-b+c/2)= sin b+c/2
  • sin b+c/2 +cosb+c/4cosb-c/4
  • 2sin b+c/4cosb+c/4 + 2cosb+c/2cosb-c/4
  • 2cosb+c/4(sinb+c/4 +cosb-c/4)
  • 2cosb+c/4 + [cos(pie/2-b+c/4) +cosb-c/4]
  • 2cosb+c/4 2cospie-c/4 cospie-b/4
  • 4cospie-a/4 cospie-b/4 cospie-c/4

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