Question

Express all trigonometric ratios in terms of cos A

Answer 1

ANSWER IS GIVEN BELOW....

Answer 2

Answer:

All trigonometric ratios in terms of cosA.

$i) sinA= \sqrt{1-cos^{2}A}$

$ii ) tanA = \frac{\sqrt{1-cos^{2}A}}{cosA}$

$iii) cot A =\frac{cosA}{\sqrt{1-cos^{2}A}}$

$iv) secA = \frac{1}{cosA}$

$v) cosecA = \frac{1}{\sqrt{1-cos^{2}A}}$

Step-by-step explanation:

$We \: know \: the \\</p><p>Trigonometric\: identity:\\\boxed {sin^{2}A = 1-cos^{2}A}$

Now ,

$i) sinA= \sqrt{1-cos^{2}A}$

$ii ) tanA = \frac{sinA}{cosA}\\=\frac{\sqrt{1-cos^{2}A}}{cosA}$

$iii) cot A = \frac{1}{tanA}\\=\frac{1}{\frac{\sqrt{1-cos^{2}A}}{cosA}}\\=\frac{cosA}{\sqrt{1-cos^{2}A}}$

$iv) secA = \frac{1}{cosA}$

$v) cosecA = \frac{1}{sinA}\\=\frac{1}{\sqrt{1-cos^{2}A}}$

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