Question

Express $\sin A$ in terms of $\cot A$.

Answer 1

Express $\sin A$ in terms of $\mathrm{cotA}$.

Since, ${\mathrm{cosec}}^{2}A=1+{\cot }^{2}A$ $...\left(i\right)$

And, ${\sin }^{2}A=\frac{1}{{\mathrm{cosec}}^{2}A}$ $...\left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$

we get,

${\sin }^{2}A=\frac{1}{1+co{t}^{2}A}$

Taking square root on both the sides, we get

$\sin A=\frac{1}{\mathrm{cosec}A}$

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

Hence, $\sin A$ in terms of $\cot A$ is written as $\frac{1}{\sqrt{1+co{t}^{2}A}}$.