Question

Write the trigonometric ration of $\sin A$ in terms of $\cot A$.

Answer 1

We know $1+{\cot }^{2}A={\text{cosec}}^{2}A$

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