Question

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

A. (tan x(1-sec x))/(1+sec x)(1-sec x)
B. tan xcos x/cos x+sec x
C. tan x+sin x

Answer 1

The acceptable first step in simplifying the expression tan x/1+sec x is to apply the identity tan x = sin x/cos x and the identity sec x = 1/cos x. This gives us (sin x/cos x)/(1 + 1/cos x). To simplify further, we can multiply the numerator and denominator by cos x to get sin x/(cos x + 1). Now, the expression is in simplified form.

Step-by-step explanation:

The acceptable first step in simplifying the expression tan x/1+sec x is to apply the identity tan x = sin x/cos x and the identity sec x = 1/cos x.

This gives us (sin x/cos x)/(1 + 1/cos x).

To simplify further, we can multiply the numerator and denominator by cos x to get sin x/(cos x + 1).

Now, the expression is in simplified form.