Which of the following would be an acceptable first step in simplifying the expression tanx/(1 + secx)
tanx(1 - secx) / (1 + secx)(1 - secx)
tanx + sinx
tanx.cosx / cosx + secx
None of the above

Solution:

Given, the expression tanx/(1 + secx)

Step 1: Multiply and divide by (1 - secx)

= [tanx (1 - secx)/ (1 + secx) (1 - secx)]

Therefore, the first step is [tanx (1 - secx)/ (1 + secx) (1 - secx)].

=tanx (1 - secx)/ (1 - sec²x)

Step 2: (tanx - tanx secx)/ tan² x

Step 3: [1- secx]/ tan x

Step 4:  1/ tan x - sec x / tan x

1/ tan x - 1/ sin x

= cot x - cosec x

Therefore, the first step is [tanx (1 - secx)/ (1 + secx) (1 - secx)].

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

Summary:

The acceptable first step in simplifying the expression tanx/(1 + secx) is [tanx (1 - secx)/ (1 + secx) (1 - secx)].