Question

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

Answer 1

(1) $\sin A=\frac{1}{cosecA}$

$=\frac{1}{\sqrt{cose{c}^{2}A}}$

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

(2) $\sec A=\sqrt{{\sec }^{2}A}$

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

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

(3) $\tan A=\frac{1}{\cot A}$