Question

for any triangle ABC prove that

Answer 1

Hey !!!

from LHS

a + b / c

we know sine formula

a/sin2A = 2E

•°• a = 2RsinA

b = 2R sinB

c = 2R sinC

therefore , 2RsinA + 2RsinB / 2R sinC

=> sinA + sinB / sinC

we know,
sinA + sinB = 2sin (A + B)/2 *cos ( A -B) /2

And sinC = 2sinc/2 cosC/2

since,

= 2sin(A + B) /2 cos ( A - B)/2
_________________________
2sinC/2 cosC /2

=2sin ( 90° - C/2) cos ( A- B)/2 ______________________
2sinC/2 cosC/2

=> cosC /2 cos ( A - B) /2
_____________________
2sinC/2 cosC/2

=> cos ( A - B )/2
_______________
cosC/2

LHS = RHS prooved ♻
__________________________

Hope it helps you !!!

@Rajukumar111