Question

7. If 5 cot A = 8, find the value of Sec A.​

Answer 1

Given

• 5 cot A = 8
• Cot A = $\dfrac{8}{5}$

To find

• Value of sec A .

Solution

• We know that

$\sf\pink{⟶}$ Cot A = $\dfrac{base}{perpendicular}$

Here,

• b = 8
• p = 5

$\sf\pink{⟶}$ We have to find hypotenuse (h).

$\tt:\implies{h = \sqrt{b^2 + p^2}}$

$\tt:\implies{h = \sqrt{(8)^2 + (5)^2}}$

$\tt:\implies{h = \sqrt{64 + 25}}$

$\tt:\implies{h = \sqrt{89}}$

⠀

We also know that

Sec A = $\dfrac{h}{b}$

⠀

$\tt:\implies{Sec A = \dfrac{\sqrt{89}}{8}}$

⠀

$\sf\pink{⟶}$ Value of Sec A is $\dfrac{\sqrt{89}}{8}$

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Answer 2

Step-by-step explanation:

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

To find: Value of $sec \: A$

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:

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

Hope it helps you.

To learn more on brainly:

Q 16. The value of is:

sec 60° - cos 30° + tan 45º

sin 60° + cot 45° - cosec 30°https://brainly.in/question/47792126

iii) cos^2 15° - cos^2 30° + cos^2 45° - cos^2 60° + cos^2 75° = 1/2

please help me solve this

https://brainly.in/question/43525162