College Math Master Math Problem

Math Problem
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We first try to solve the first problem. In one rotation of the wheel the distance traveled by it when it rolls along a road is equal to the circumference of the wheel. In other words when the wheel travels a distance equal to its circumference it completes one rotation.


The difference in their weight, if any, is assumed to be insignificant enough not to contribute any significant difference in wearing out of the tires.
We also know that tan(90) is undefined and so also tan((4n+1).90) where n is any positive integer. Therefore, tan(450) = tan((4X1+1)90) is undefined. Therefore, the right hand side of the above equation will be undefined and hence tan(x + 450) cannot be simplified using the tangent sum formula.
But sin(x + 450) = cos(x) and cos(450 + x) = -sin(x) as x + 450 is located in second quadrant. Therefore tan(x + 450) = sin(x + 450) / cos(x + 450) = cos(x) / - sin(x) = -cot(x). since sin and cos are defined for all real numbers and the problem is only with tan as it is not defined for certain real numbers((4n+1)90, (4n-1)90, -(4n+1)90, -(4n-1)90) tan(x + 450) cannot be simplified using tangent sum formula but can be simplified using sin and cos formulas.
We now attempt to differentiate between the trigonometric equation that is identity and the trigonometric equation that is not identity. We have from symbolic logic the definition of identity as x is said to be identical with y if x takes a value "u" implies y takes the value "u". ...
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