Question

Express the trigonometric ratios $\sin A,\sec A$ and $\tan A$ in terms of $\cot A$.

Answer 1

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

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

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

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