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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)`
Solution
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`
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