Question

give me ANSWER= Proof that
cotA/2-tanA/2=2cotA

Answer 1

cot A/2-tan A/2
= (cos A/2)/(sin A/2) - (sin A/2)/(cos A/2)
= {(cos A/2)² - (sin A/2)²} / (sin A/2 cos A/2)
= cos A / (sin A/2 cos A/2) ... half angle formula
= 2cosA / (2sin A/2 cos A/2) ... multiply divide by 2
= 2 cot A ... half angle formula

...thus proved

Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

$\textbf{To Prove : }\cot\frac{A}{2}-\tan\frac{A}{2}=2\cot A$

Proof : Taking L.H.S. first

$=\cot\frac{A}{2}-\tan\frac{A}{2}\\\\=\frac{\cos\frac{A}{2}}{\sin\frac{A}{2}}-\frac{\sin \frac{A}{2}}{\cos\frac{A}{2}}\\\\=\frac{\cos^2\frac{A}{2}-\sin^2\frac{A}{2}}{\sin\frac{A}{2} \cdot \cos\frac{A}{2}}\\\\=\frac{\cos A}{\sin\frac{A}{2} \cdot \cos\frac{A}{2}}\\\\= \frac{ 2\cos A}{2\sin\frac{A}{2} \cdot \cos\frac{A}{2}}\\\\=\frac{2\cos A}{\sin A}\\\\=2\cot A$

= R.H.S.

Hence Proved