Question

If A,B,C are angles of triangles . Cot(B+C / 2) then is equal to-​

Answer 1

$\large \underline \bold{Solution}$:-

$\sf{A \: , \: B \: and \: C \: are \: the \: angles \: of \: a \: triangle \: ABC .}$

$\small \underline \bold{We \: know \: that}$-

$\sf{The \: sum \: of \: all \: three \: angles \: of \: a \: triangle \: is \: 180.}$

$\sf{So \: ,}$

$\small \underline \bold{Step \: I}$:-

$\: \: \: \: \:$$\sf{A + B + C = 180}$°

$\small \underline \bold{Step \: II}$:-

$\: \: \: \: \:$$\sf{(B + C) = 180 - A}$

$\small \underline \bold{Step \: III}$:-

$\: \: \: \: \:$$\sf{\dfrac{(B + C)}{2} = \dfrac{(180 - A)}{2}}$

$\: \: \: \: \:$$\sf{\dfrac{(B + C)}{2} = (90 - \dfrac{A}{2})}$

$\small \underline \bold{Step \: IV}$:-

$\: \: \: \: \:$$\sf{Cot\dfrac{(B + C)}{2} = Cot(90 - \dfrac{A}{2})}$

$\large \underline \bold{We \: know \: that}$-

$\: \: \: \: \:$$\sf{Cot(90 - x) = tanx}$

$\sf{So \: ,}$

$\small \underline \bold{Step \: V}$:-

$\: \: \: \: \:$$\sf{Cot\dfrac{(B + C)}{2} = tan\dfrac{A}{2}}$