Question

I need help from uh all..​

Answer 1

Answer:

Step-by-step explanation:

Given expression is,

$\text{cot}A=\frac{1}{2}(\text{cot}\frac{A}{2}-\text{tan}\frac{A}{2})$

To prove this identity we will take the right side of the identity,

$\frac{1}{2}(\text{cot}\frac{A}{2}-\text{tan}\frac{A}{2})=\frac{1}{2}(\frac{1}{\text{tan}\frac{A}{2}}-tan\frac{A}{2})$

                         $=\frac{1}{2}(\frac{1-\text{tan}^2\frac{A}{2}}{tan\frac{A}{2}})$

                         $=\frac{1}{2}[\frac{2(1-\text{tan}^2\frac{A}{2})}{2tan\frac{A}{2}}]$

                         $=\frac{1}{2}(\frac{2}{\text{tan}A} )$ [Since $\text{tan}A=\frac{2\text{tan}\frac{A}{2}}{1-\text{tan}^2\frac{A}{2}}$]

                         = cot A

Hence right side of the equation is equal to the left side of the equation.