Question

Write the other trigonometric ratios of A in terms of sec A.

Answer 1

All trigonometric ratios of LA in terms of sec A

$\cos A=\frac{1}{secA}$

$\tan A$

we know that ${\sec }^{2}A={\tan }^{2}A=1$

${\tan }^{2}A={\sec }^{2}A-1$

$\tan A=\sqrt{{\sec }^{2}A-1}$

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

$cosecA$

$1+{\cot }^{2}A=cose{c}^{2}A$

$1+(\frac{1}{\sqrt{se{c}^{2}A-1}}{)}^2=cose{c}^{2}A$

$\frac{{\sec }^{2}A-1+x}{{\sec }^{2}A-1}=cose{c}^{2}A$

$cosecA=\pm \frac{\sec A}{\sqrt{{\sec }^{2}A-1}}$

$\sin A=\frac{1}{cosecA}=\frac{1}{\pm \frac{\sec A}{\sqrt{{\sec }^{2}A-1}}}$

$\sin A=\pm \frac{\sqrt{{\sec }^{2}A-1}}{\sec A}$