Question

Oliver incorrectly states that the expression tan(3pi/4 + x) can be simplified as -1. Review Oliver’s work. Which statement explains why Oliver is incorrect?
Keyword gibberish:
The expression does not simplify not have a value if simplified to not equivalent to not
tan startfraction 3 pi over 4 endfraction + x

Answer 1

We want to see where Oliver is making a mistake in his claim.

The correct option is the first one, the simplification on the last step is wrong.

We start with the expression:

$tan( \frac{3*pi}{4} + x)$

Now, by looking at Olvier's work, we can see that on the last step he writes:

$\frac{-1 + tan(x)}{1 + tan(x)} = -1$

This is clearly wrong, as the numerator and the denominator are dont simplify to -1 (this only happens if the numerator is -1 times the denominator), so the left side can't be equal to -1, it actually would be simplified to:

$\frac{-1 + tan(x)}{1 + tan(x)} = \frac{-1 +1 - 1 tan(x)}{1 + tan(x)} = \frac{-2 + 1 + tan(x)}{1 + tan(x)} \\\\\frac{-2 + (1 + tan(x))}{1 + tan(x)} = \frac{-2 }{1 + tan(x)} + \frac{ 1 + tan(x)}{1 + tan(x)} = \frac{-2 }{1 + tan(x)} + 1$

Then the correct option is the first option.

If you want to learn more, you can read:

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