Question

prove that cot2A = cot square A - 1 /2cotA

Answer 1

I've used the formula of tan2a to prove the above que . u can also do without it

Answer 2

Solution:

Given: $\cot 2 A=\frac{\cot ^{2}(A-1)}{2 \cot A}$   (Obtained from the formula)  

Now, $\cot =\frac{1}{\tan }$

Therefore,$\cot 2 A=\frac{1}{\tan 2 A}$

$\cot 2 A=\frac{1}{\tan 2 A}$ (from the previous step)

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

$\frac{1}{\tan 2 \mathrm{A}}=\frac{1-\tan ^{2}(\mathrm{A})}{2 \tan A}$   (forming the reciprocal of the given values)

Substitute $\tan A=\frac{1}{\cot A}$

$\cot 2 A=\frac{1-\left(\frac{1}{\cot ^{2} A}\right)}{2\left(\frac{1}{\cot A}\right)}$ ( by formula)

$\bold{\begin{array}{l}{=\frac{\cot ^{2} A-1}{\cot ^{2} A} \times \frac{\cot A}{2}} \\ \\ {\cot 2 A=\frac{\cot ^{2} A-1}{2 \cot A}}\end{array}}$

Hence Proved.