Question

If A, B  and C are the angles of a  ΔABC, prove that tan `((C + "A")/2) = cot  B/2`

Answer 1

In ΔABC 

A + B + c = 180° 

⇒ A + C = 180° - B      ..........(i)

Now,

LHS `= tan (("C"+"A")/2)`

`=tan ((180^circ - "B")/2)`           [Using (i)]

`= tan (90^circ - "B"/2)`

`= cot  "B"/2 `

= RHS