Question

If tan x =15/12, then find sec x.​

Answer 1

Answer:

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Answer 2

Given:

$\tan (x)= \dfrac{15}{12}$

To Find:

$\sec (x)$

Explanation:

$\text{We know that } \tan (x) = \dfrac{\text{Opposite}}{\text{Adjaccent}}$

$\implies \text{ opposite} = 15$

$\implies \text{ adjacent} = 12$

Solution:

Find the hypotenuse of the triangle:

$a^2 + b^2 = c^2$

$c^2 = a^2 + b^2$

$c^2 = (15)^2 + (12)^2$

$c^2 = 369$

$c = 3\sqrt{41}$

Find cos x:

$\cos (x) = \dfrac{\text{opposite}}{\text{hypotenuse}}$

$\cos (x) = \dfrac{15}{3\sqrt{41} }$

$\cos (x) = \dfrac{5\sqrt{41} }{41}$

Find sec x:

$\sec (x) = \dfrac{1}{\cos (x)}$

$\sec (x) = \dfrac{41}{5\sqrt{41} }$

$\sec (x) = \dfrac{\sqrt{41} }{5}$