Question

Write all the other trigonometric ratios of A in terms of secA.

Answer 1

$\sec A=\frac{1}{\cos A}\Rightarrow \cos A=\frac{1}{\sec A}$

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

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

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

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