The acceptable first step in simplifying the expression [tex]\mathbf{\frac{tan\ x}{1 + sec\ x}}[/tex] is (a) [tex]\mathbf{\frac{tan\ x(1 - sec\ x)}{(1 + sec\ x)(1 - sec\ x)}}[/tex]
The expression is given as:
[tex]\mathbf{\frac{tan\ x}{1 + sec\ x}}[/tex]
To change the form of the expression, we simply perform several arithmetic operations on it.
Start by multiplying the expression by 1/1
[tex]\mathbf{\frac{tan\ x}{1 + sec\ x} = \frac{tan\ x}{1 + sec\ x} \times \frac 11}[/tex]
Express 1 /1 as (1 - sec x)/(1 - sec x)
[tex]\mathbf{\frac{tan\ x}{1 + sec\ x} = \frac{tan\ x}{1 + sec\ x} \times \frac{1 - sec\ x}{1 - sec\ x}}[/tex]
Rewrite the above expression as follows:
[tex]\mathbf{\frac{tan\ x}{1 + sec\ x} = \frac{tan\ x(1 - sec\ x)}{(1 + sec\ x)(1 - sec\ x)}}[/tex]
Hence, the acceptable first step is (a)
Read more about trigonometry ratios at:
https://brainly.com/question/24888715
