Question

Question 2
Write all the other trigonometric ratios of $\angle$A in terms of sec A.

Answer 1

We know that,
sec A = 1/cos A
$\Rightarrow$ cos A = 1/sec A
Also,
$co{s}^{2}A+si{n}^{2}A=1$
$\Rightarrow si{n}^{2}A=1-co{s}^{2}A$
$\Rightarrow si{n}^{2}A=1-\left(1/se{c}^{2}A\right)$
$\Rightarrow si{n}^{2}A=(se{c}^{2}A-1)/se{c}^{2}A$
$\Rightarrow sinA=\frac{\pm \sqrt{se{c}^{2}A-1}}{\sec A}$
sin A = 1/cosec A
$\Rightarrow$ cosec A = 1/sin A
$\Rightarrow cosecA=\frac{\pm secA}{\sqrt{se{c}^{2}A-1}}$
$se{c}^{2}A-ta{n}^{2}A=1$
$\Rightarrow ta{n}^{2}A=se{c}^{2}A-1$
$\Rightarrow tanA=\pm \sqrt{se{c}^{2}A-1}$
tan A = 1/cot A
$\Rightarrow$ cot A = 1/tan A
$\Rightarrow cotA=\frac{\pm 1}{\sqrt{se{c}^{2}A-1}}$