Question

A+B+C = 180° cosA+ cos' B+cos C=​

Answer 1

Answer:

The answer is -1 + 4 cos A/2 cos B/2 cos C/2

Step-by-step explanation:

Answer 2

Answer:

A+B+C=m……(1)

L.H.S.

=(cosA+cosB)+cosC

={2⋅cos[(A+B)/2]⋅cos[(A−B)/2]}+cosC

={2⋅cos[(π/2)−(C/2)]⋅cos[(A−B)/2]}+cosC

={2⋅sin(C/2)⋅cos[(A−B)/2]}+(1−2⋅sin2(C/2)]

=1+2sin(C/2)⋅(cos[(A−B)/2]−sin(C/2)}

=1+2sin(C/2)⋅(cos[(A−B)/2]−sin[(π/2)−((A+B)/2)]}

=1+2sin(C/2)⋅(cos[(A−B)/2]−cos[(A+B)/2]}

=1+2sin(C/2)⋅2sin(A/2)⋅sin(B/2)………(2)  

=1+4sin(A/2)sin(B/2)sin(C/2)

=R⋅H.S