Question

2 cotθ= 4cosθ, find the value of sec2θ+tan2θ.
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Answer 1

Step-by-step explanation:

GIVEN :

$2 \cot(x) = 4 \cos(x) \\ 2 \frac{ \cos(x) }{ \sin(x) } = 4 \cos(x) \\ \frac{1}{ \sin(x) } = 2 \\ \sin(x) = \frac{1}{2}$

$hence \\ x = 30$

because sin30°=1/2

to find :

$\sec(2x) + \tan(2x)$

$= \sec(2x) + \tan(2x) \\ = \sec(2(30)) + \tan(2(30)) \\ = \sec(60) + \tan(60) \\ = 2 + \sqrt{3} \\ = 2 + 1.73 \\ = 3.73$

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