Question

prove that : cot A/2- tan A/2=2cotA​

Answer 1

Answer:

sorry can't proove

Step-by-step explanation:

don't know

Answer 2

Answer:

RHS

Step-by-step explanation:

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 ATo Prove : cot2A−tan2A=2cotA

Proof : Taking L.H.S. first

\begin{gathered}=\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\end{gathered}=cot2A−tan2A=sin2Acos2A−cos2Asin2A=sin2A⋅cos2Acos22A−sin22A=sin2A⋅cos2AcosA=2sin2A⋅cos2A2cosA=sinA2cosA=2cotA

= R.H.S.

Hence Proved