Question

Which of the following would be an acceptable first step in simplifying the expression tanx/1+ secx

Answer 1

The acceptable first step in simplifying the expression $\mathbf{\frac{tan\ x}{1 + sec\ x}}$ is (a) $\mathbf{\frac{tan\ x(1 - sec\ x)}{(1 + sec\ x)(1 - sec\ x)}}$

The expression is given as:

$\mathbf{\frac{tan\ x}{1 + sec\ x}}$

To change the form of the expression, we simply perform several arithmetic operations on it.

Start by multiplying the expression by 1/1

$\mathbf{\frac{tan\ x}{1 + sec\ x} = \frac{tan\ x}{1 + sec\ x} \times \frac 11}$

Express 1 /1 as (1 - sec x)/(1 - sec x)

$\mathbf{\frac{tan\ x}{1 + sec\ x} = \frac{tan\ x}{1 + sec\ x} \times \frac{1 - sec\ x}{1 - sec\ x}}$

Rewrite the above expression as follows:

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

Hence, the acceptable first step is (a)

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Answer 2

Answer:

A

Step-by-step explanation:

The possible first step is A