Answer:
[tex]\dfrac{1}{\tan^2(\theta)}}=\cot^2(\theta)[/tex]
Step-by-step explanation:
[tex]\cot(\theta)=\dfrac{1}{\tan(\theta)}[/tex]
[tex]\implies \dfrac{\cot(\theta)}{\tan(\theta)}=\dfrac{1}{\tan(\theta)}\div{\tan(\theta)}}=\dfrac{1}{\tan(\theta)} \times \dfrac{1}{\tan(\theta)} =\dfrac{1}{\tan^2(\theta)}}=\cot^2(\theta)[/tex]
[tex]\\ \rm\Rrightarrow cotA\div tanA[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{cosA}{sinA}\div \dfrac{sinA}{cosA}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{cosA}{sinA}\times \dfrac{cosA}{sinA}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{cos^2A}{sin^2A}[/tex]
[tex]\\ \rm\Rrightarrow cot^2A[/tex]
Note
