Question

in a triangleABC, tan(A+C/2)=​

Answer 1

Answer:

sum of all angles of triangle=180°

A+B+C=180°

A+C=180-B

=tan(180-B) /2

= -tanB/2

helpful to all mark as brainlest answer

Answer 2

Step-by-step explanation:

Given :-

In ∆ ABC , A,B,C are the three interior angles.

To find :-

Find the value of Tan (A+C)/2 ?

Solution :-

Given that

In ∆ ABC , A,B,C are the three interior angles.

We know that

The sum of all the three angles in a triangle is 180°

=> A+B+C = 180°

On dividing by 2 both sides then

=> (A+B+C) /2 = 180°/2

=> (A+B+C) /2 = 90°

=> (A+C)/2 +( B/2) = 90°

=> (A+C)/2 = 90°-(B/2)

On taking Tan ratio both sides then

=> Tan (A+C)/2 = Tan [90°-(B/2)]

=> Tan (A+C)/2 = Cot (B/2)

Since Tan (90°- θ) = Cot θ

Answer:-

Tan (A+C)/2 = Cot (B/2)

Used formulae:-

→ The sum of all the three angles in a triangle is 180°

→ Tan (90°- θ) = Cot θ