We are given the equation $Sem(5 \times 21) = cos(9^\circ) + tan(5x)$ and we need to find the value of $x$. I assume that $Sem$ represents the semiperimeter.

1. Problem Description

We are given the equation $Sem(5 \times 21) = cos(9^\circ) + tan(5x)$ and we need to find the value of $x$. I assume that $Sem$ represents the semiperimeter.

2. Solution Steps

First, calculate the value of $5 \times 21$.

$5 \times 21 = 105$

So the equation becomes $Sem(105) = cos(9^\circ) + tan(5x)$.

Since $Sem$ is the semiperimeter, it is not a function, and the semiperimeter of 105 is not uniquely defined.

However, I assume that we are working in degrees.

I also assume that $Sem(x)$ means $\sin(x)$. This is the only way the problem makes sense.

Then the equation is $\sin(105^\circ) = \cos(9^\circ) + \tan(5x)$.

We know that $\sin(105^\circ) = \sin(180^\circ - 105^\circ) = \sin(75^\circ)$

And $\sin(75^\circ) = \sin(45^\circ + 30^\circ) = \sin(45^\circ)\cos(30^\circ) + \cos(45^\circ)\sin(30^\circ)$

$= \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2} = \frac{\sqrt{6} + \sqrt{2}}{4}$

We also have $\cos(9^\circ)$. Using a calculator, $\cos(9^\circ) \approx 0.987688$.

Also $\sin(105^\circ) \approx 0.965926$.

Then the equation becomes $0.965926 \approx 0.987688 + \tan(5x)$.

So $\tan(5x) \approx 0.965926 - 0.987688 = -0.021762$.

So $5x = \arctan(-0.021762)$.

$5x \approx -1.2469^\circ$

$x \approx -0.24938^\circ$

If we assume that $Sem(x)$ stands for simply $x$, then the equation is $105 = \cos(9^\circ) + \tan(5x)$.

$105 - \cos(9^\circ) = \tan(5x)$

$105 - 0.987688 = \tan(5x)$

$104.012312 = \tan(5x)$

$5x = \arctan(104.012312)$

$5x = 89.45085^\circ$

$x = 17.89017^\circ$

If $Sem(x)$ stands for $\sin(x)$, and all the angles are in radians, then

$\sin(105) = \cos(9) + \tan(5x)$

$-0.94023 \approx 0.9912 + \tan(5x)$

$\tan(5x) \approx -1.93143$

$5x \approx -1.09452$

$x \approx -0.2189$ radians

$x \approx -12.545$ degrees.

3. Final Answer

Assuming $Sem(x) = sin(x)$ and the angles are in degrees, $x \approx -0.24938^\circ$.

Assuming $Sem(x) = x$ and the angles are in degrees, $x \approx 17.89017^\circ$.