Question

If P, Q and R are the interior angles of ΔPQR, prove that `cot(("Q" + "R")/2) = tan  "P"/(2)`

Answer 1

Since P, Q and R are interior angles of ΔPQR,
P + Q + R = 180°
⇒ Q + R = 180° - P
Now,
L.H.S. = `cot (("Q" + "R")/2)`

= `cot ((180° - "P")/2)`

= `cot(90° - "P"/2)`

= `tan  "P"/(2)`
= R.H.S.