Question

lf A, B and C are the interior angles of a triangle ABC, show that:

1-) cos A + B/2 = sin C/2

2-) tan C + A/2 = cot B/2​

Answer 1

Step-by-step explanation:

answer 1)

cos ( a+b/2) = sin (c/2).

LHS :

cos ( 180- c/2). ........

( by angle sum property of triangle a+b+c =180....so from here we get a+b = 180-c)

cos ( 180/2 - c/2)

cos ( 90 -c/2).

then finally we get,

sin ( c/2).

( because cos ( 90- theta ) = sin theta )..

answer 2).

in the same way by angle sum property .

a+b+c =180.

c+a =180-b.

LHS:

tan (c+a/2) = cot ( b/2).

tan ( 180-b/2).

tan (180/2 -b/2).

tan ( 90 -b/2).

hence. cot(b/2).

because , tan ( 90-theta )= cot theta...

HOPE THIS WILL HELP U......Just remember the complementory identities