Question

if 5 cot A=8, then the value of sinA and secA is​

Answer 1

Step-by-step explanation:

$\cot( \alpha ) = \frac{8}{5} \\ = > \frac{base}{perpendicuar} = \frac{8}{5} \\ \\ = > height = \sqrt{{8}^{2} + {5}^{2} } = \sqrt{64 + 25} = \sqrt{89}$

$\sin( \alpha ) = \frac{perpendicular}{height} = \frac{5}{ \sqrt{89} }$

$\cos( \alpha ) = \frac{base}{height} = \frac{8}{ \sqrt{89} }$

$\sec( \alpha ) = \frac{1}{ \cos( \alpha ) } = \frac{ \sqrt{89} }{8}$

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Answer 2

Step-by-step explanation:

Given: $5 \: cot \: A = 8$

To find: Value of $sinA\: \: and \: sec \: A$

Solution:

Identities used:

$1)\:1 + {cot}^{2} A = {cosec}^{2}A$

$2)\:sin \: A = \frac{1}{cosec \: A}$

$3)\:1 - {sin}^{2} A= {cos}^{2} A$

$4)\:sec \: A = \frac{1}{cos \: A}$

Step 1: Find $sin \: A$

Use identity 1 and 2 written above.

$1 + \frac{64}{25} = {cosec}^{2}A$

${cosec}^{2} A= \frac{25 + 64}{25}$

$cosec\:A= \frac{ \sqrt{89} }{5}$

Thus,

$sin \: A = \frac{5}{ \sqrt{89} }$

Step 2: Find $sec\:A$

Use identity 3 and 4.

${cos}^{2} A = 1 - \frac{25}{89}$

${cos}^{2} A = \frac{89 - 25}{89}$

$cos \: A = \frac{8}{ \sqrt{89} }$

Thus,

$sec \: A = \frac{ \sqrt{89} }{8}$

Final answer:

$\bf \green{sin \: A = \frac{5}{ \sqrt{89} }}$

$\bf \red{sec \: A = \frac{ \sqrt{89} }{8}}$

Hope it helps you.

To learn more on brainly:

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