Question

Express the trignometric ratios sinA , secA and tan A interms of cotA.

Answer 1

$\left(1\right)$
$\sin A$ in terms of $\cot A:$

$\sin A=\frac{1}{\csc A}$

We know that

${\csc }^{2}A=1+{\cot }^{2}A$

$\sin A=\frac{1}{\sqrt{1+{\cot }^{2}A}}$

$\left(2\right)$

$\sec A$ in terms of $\cot A$:

We know that

$1+{\tan }^{2}A={\sec }^{2}A$

${\sec }^{2}A=1+{\tan }^{2}A$

${\sec }^{2}A=1+\frac{1}{{\cot }^{2}A}$

${\sec }^{2}A=\frac{({\cot }^{2}A+1)}{{\cot }^{2}A}$

$\sec A=\frac{\sqrt{({\cot }^{2}A+1)}}{\cot A}$

$\left(3\right)$

$\tan A$ in terms of $\cot A$:

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

Hence, this is the answer.