Question

solve the question of math

Answer 1

answer in the picture

Answer 2

If there is a cosine function involved, it indicates that there is right angle triangle. With a base, a height and a hypotenuse.

So,
$\cos{A} = \frac25$
Then, by definition,
base = 2 units
hypotenuse = 5 units

So, the height =
$\sqrt{5^2 - 2^2}$
= $\sqrt{21} units$

So,
$\tan{A} = \dfrac{height}{base}$
or, $\tan{A} = \dfrac{\sqrt{}21}{2}$
or, $\tan^2{A} = \dfrac{21}{4}$

So, $4 + 4\tan^2{A} = 4 + 4 \times \dfrac{21}{4} = 4 +21 = 25$

So, the answer is 25.

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