If secA+tanA=x, then the value of x is:

Note: Options B and D represent the same simplified algebraic form, let's verify by simplifying the original expression:
Given:

x=secA+tanA
Expressing in terms of sine and cosine:

x=
cosA
1
​
+
cosA
sinA
​
=
cosA
1+sinA
​

Now let's multiply the numerator and the denominator by (1−sinA) to see if it matches any of the rationalized choices:

x=
cosA(1−sinA)
(1+sinA)(1−sinA)
​

x=
cosA(1−sinA)
1−sin
2
A
​

Since 1−sin
2
A=cos
2
A:

x=
cosA(1−sinA)
cos
2
A
​
=
1−sinA
cosA
​

This corresponds precisely to
1−sinA
cosA
​
, which is listed in option D (and option B). Thus, the correct answer option is D.