(Solved): 1 green Establish the identity. \[ \cot (2 \theta)=\frac{\cot ^{2} \theta-1}{2 \cot \theta} \] Choos ...

Establish the identity. \[ \cot (2 \theta)=\frac{\cot ^{2} \theta-1}{2 \cot \theta} \] Choose the sequence of steps below that verifies the identity. A. \( \cot (2 \theta)=\frac{1}{\tan (20)}=\frac{1-\tan \theta}{2 \tan ^{2} \theta}=\frac{1-\frac{1}{\cot \theta}}{\frac{2}{\cot ^{2} \theta}}=\frac{\cot \theta-1}{\cot \theta} \cdot \frac{\cot ^{2} \theta}{2}=\frac{\cot ^{2} \theta-1}{2 \cot \theta} \) B. \( \cot (2 \theta)=\frac{1}{\tan (20)}=\frac{1+\tan ^{2} \theta}{\tan \theta}=\frac{1+\frac{1}{\cot ^{2} \theta}}{\frac{2}{\cot \theta}}=\frac{\cot ^{2} \theta+1}{\cot ^{2} \theta} \cdot \frac{\cot \theta}{2}=\frac{\cot ^{2} \theta-1}{2 \cot \theta} \) C. \( \cot (2 \theta)=\frac{1}{\tan (20)}=\frac{1-\tan ^{2} \theta}{2 \tan \theta}=\frac{1-\frac{1}{\cot ^{2} \theta}}{\frac{2}{\cot \theta}}=\frac{\cot ^{2} \theta-1}{\cot ^{2} \theta} \cdot \frac{\cot \theta}{2}=\frac{\cot ^{2} \theta-1}{2 \cot \theta} \) D. \( \cot (2 \theta)=\frac{1}{\tan (2 \theta)}=\frac{2 \tan \theta}{1-\tan ^{2} \theta}=\frac{\frac{2}{\cot \theta}}{1-\frac{1}{\cot ^{2} \theta}}=\frac{2}{\cot \theta} \cdot \frac{\cot ^{2} \theta-1}{\cot ^{2} \theta}=\frac{\cot ^{2} \theta-1}{2 \cot \theta} \)