Answer:
Step-by-step explanation:
Given expression is,
[tex]\text{cot}A=\frac{1}{2}(\text{cot}\frac{A}{2}-\text{tan}\frac{A}{2})[/tex]
To prove this identity we will take the right side of the identity,
[tex]\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})[/tex]
[tex]=\frac{1}{2}(\frac{1-\text{tan}^2\frac{A}{2}}{tan\frac{A}{2}})[/tex]
[tex]=\frac{1}{2}[\frac{2(1-\text{tan}^2\frac{A}{2})}{2tan\frac{A}{2}}][/tex]
[tex]=\frac{1}{2}(\frac{2}{\text{tan}A} )[/tex] [Since [tex]\text{tan}A=\frac{2\text{tan}\frac{A}{2}}{1-\text{tan}^2\frac{A}{2}}[/tex]]
= cot A
Hence right side of the equation is equal to the left side of the equation.
