Question

if a+b+c=180° then prove tan (a–b/2) = cot (c/2+b)​

Answer 1

Answer:

hope it helps you

Step-by-step explanation:

a+b+c=180°

required to prove is tan(a-b/2)=cot(c/2+b)

 add -b on bothsides to a+b+c=180°

      a+b+c-b=180°-b

             a-b =180°-b-b-c

             a-b=180°-2b-c

  divide by 2 on both sides

          a-b/2=(180°-2b-c)/2    

          a-b/2=90°-b-(c/2)

apply tan on both sides

  tan(a-b/2)=tan(90°-b-(c/2))

                  =cot(b-c/2)  

         ∵tan(90°-θ)=cotθ