$$ 1600-5 x+0 {} \frac{1+\operatorname{Cin} A}{1- an A}=\frac{\operatorname{Cos} A+\operatorname{Sen} A}{\operatorname{Cos} A-\operatorname{Sin} A} $$

Question

$$ 1600-5 x+0 {} \frac{1+\operatorname{Cin} A}{1-	an A}=\frac{\operatorname{Cos} A+\operatorname{Sen} A}{\operatorname{Cos} A-\operatorname{Sin} A} $$

UpStudy AI · Accepted Answer

We start with the equation
$$
1600-5x+0\cdot\frac{1+\operatorname{Cin}A}{1-\tan A}=\frac{\operatorname{Cos}A+\operatorname{Sen}A}{\operatorname{Cos}A-\operatorname{Sin}A}\,.
$$
Notice that the term
$$
0\cdot\frac{1+\operatorname{Cin}A}{1-\tan A}
$$
is equal to $$0$$ regardless of its value. Therefore, the equation simplifies to
$$
1600-5x=\frac{\cos A+\sin A}{\cos A-\sin A}\,.
$$

Next, we isolate $$x$$. Subtract $$1600$$ from both sides:
$$
-5x=\frac{\cos A+\sin A}{\cos A-\sin A}-1600\,.
$$
Now, divide both sides by $$-5$$ to solve for $$x$$:
$$
x=\frac{1600-\frac{\cos A+\sin A}{\cos A-\sin A}}{5}\,.
$$

We can also express the answer as
$$
x=320-\frac{1}{5}\cdot\frac{\cos A+\sin A}{\cos A-\sin A}\,.
$$

This is the solution for $$x$$ in terms of $$A$$.
$$ x = 320 - \frac{1}{5} \cdot \frac{\cos A + \sin A}{\cos A - \sin A} $$

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