Question

Prove that cosA÷2+cosB÷2-cosC÷2=4cospie+A÷4 cospie+B÷2cospie-C÷4

Answer 1

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