Question

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

• A. $\frac{\sqrt{1+{\cot }^{2}A}}{\cot A}$
• B. $\sqrt{\frac{1+{\cot }^{2}A}{\cot A}}$
• C. $\frac{1}{\sqrt{1+{\cot }^{2}A}}$
• D. $\frac{\sqrt{1-{\cot }^{2}A}}{\cot A}$

Answer 1

The correct option is C $\frac{1}{\sqrt{1+{\cot }^{2}A}}$

we know that

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

and

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