Question

In a right triangle ABC prove that Cos A + B by 2 is equal to sin C by 2​

Answer 1

Cos (A+B) / 2

= Sin (90-A-B)/2

= Sin C/2

Answer 2

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using sine formula ,

a/sinA =b/sinB =c/sinC =k(say)

,a =ksinA, b =ksinB, c =ksinC

LHS

(a+b)/c = (ksinA +ksinB)/ksinC

=k(2.sin(A+B)/2).cos(A-B)/2)

/(2.sinC/2.cosC/2)

= (sin(π/2-C/2).cos(A-B/2))

/(sinC/2.cosC/2)

=(cosC/2.cos(A-B/2))

/(sinC/2.cosC/2

=cos((A-B)/2)/sin(C/2)=RHS