Question

which of the following would be an acceptable first step in simplifying the expression tan^x/1+sec^x

Answer 1

The first step is replacing the given trigonometric functions by simpler ones and then taking the product of the denominators.

Which is the first step to simplifying the given expression?

Here we have the expression:

$\frac{tan(x)}{1 + sec(x)}$

Remember that:

$tan(x) = \frac{sin(x)}{cos(x)}\\ \\sec(x) = \frac{1}{cos(x)}$

Replacing that would be the "step zero", we can write:

$\frac{tan(x)}{1 + sec(x)} = tan(x)*\frac{1}{1 + sec(x)} = \frac{sin(x)}{cos(x)} \frac{1}{1 + \frac{1}{cos(x)} }$

The first step to simplify this, is taking the product between the denominators:

$\frac{sin(x)}{cos(x)} \frac{1}{1 + \frac{1}{cos(x)} } = sin(x)*\frac{1}{cos(x) + \frac{cos(x)} {cos(x)} } = \frac{sin(x)}{cos(x) + 1}$

If you want to learn more about trigonometric functions:

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Answer 2

Answer:

tanx(1-secx)/(1+secx)(1-secx)

Step-by-step explanation:

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