Question

A, B and C are interior angles of a triangle ABC. Show that

If ∠A = 90°, then find the value of tan`(("B+C")/2)`

If A, B and C, are the interior angles of a triangle ABC, prove that if ∠A = 90°, then find the value of tan`((B + C)/2)`.

Answer 1

Given: ∠ A = 90°,
∠A + ∠B + ∠C = 180°

∠B + ∠C = 180° − ∠A

`(angle"B"+angle"C")/2 =90° - (angle"A")/2`

⇒ `tan ((angle"B"+angle"C")/2) = tan(90° - (angle"A")/2)`

⇒ `tan ((angle"B"+angle"C")/2) = cot ((angle"A")/2)`

⇒ `tan ((angle"B"+angle"C")/2) = cot  ((90°)/2) = cot 45°`

⇒ `tan ((angle"B"+angle"C")/2) = 1`