Question

Trigonometry problem: if A+B+C=π then prove: cos^2 A/2+ cos^2 B/2+ cos^2 C/2= 2(1+sin A/2. sin B/2. sin C/2)?

Answer 1

Answer:

A+B+C=π

provethat:

cos

2

A+cos

2

B−cos

2

C=1−sinA.sinB.cosC

cos

2

A+sin

2

C−sin

2

B

1−sinA+sinA.cos(C−B)

1−sinA[−sin(C−B)+sinA]

1−sinA[−sin(B+C)+sin(B−C)]

1−sinA2sinBcosC

=1−2sinAsinBcosC

Hence,

proved