If A, B & Care interior angles of the triangle ABC, find the
tan(A+B/2) Value in term of cot' c' s
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Step-by-step explanation:
Given:-
A, B and C are interior angles of the triangle ABC
To find:-
Find the value of Tan(A+B)/2 in term of Cot C ?
Solution:-
Given that
A, B and C are interior angles of the ∆ ABC
We know that
Angle Sum Property:
" The sum of all interior angles in a triangle is 180°".
∠A + ∠ B + ∠ C = 180°
=> A + B + C = 180°
On dividing by 2 both sides
=> (A + B + C) / 2 = 180°/2
=> A/2 + B/2 + C/2 = 90°
=> A/2 + B/2 = 90° - C/2
=> (A+B)/2 = 90° - C/2
On taking "Tan" ratio both sides then
=> Tan (A+B)/2 = Tan( 90° - C/2)
We know that
Tan (90°- A) = Cot A
Tan (A+B)/2 = Cot C/2
Answer:-
The value of Tan (A+B)/2 for the given problem is
Cot C/2
Used formulae:-
- The sum of all interior angles in a triangle is 180°".
- Tan (90°- A) = Cot A
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