If A, B and C are interior angles of ΔABC, prove that sin ( A + B 2 ) = cos C 2 - Mathematics

If A, B and C are interior angles of ΔABC, prove that sin`(("A" + "B")/2) = cos "C"/(2)`

Sum

Since A, B and C are interior angles of ΔABC,
A + B + C = 180°
⇒ A + B = 180° - C
Now,
L.H.S. = `sin (("A" + "B")/2)`

= `sin ((180° - "C")/2)`

= `sin(90° - "C"/2)`

= `cos "C"/(2)`
= R.H.S.

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