How can we express sec x in terms of tan x?

To express sec x in terms of tan x, we can use the relationship between these trigonometric functions. Remember that:

1. The secant function is defined as the reciprocal of the cosine function: sec x = 1/cos x.

2. The tangent function is defined as the ratio of the sine to the cosine function: tan x = sin x/cos x.

We also know from the Pythagorean identity that:

1 + tan² x = sec² x.

From this identity, we can derive sec x in terms of tan x:

1. Start with the identity: sec² x = 1 + tan² x.
2. Take the square root of both sides: sec x = √(1 + tan² x).

Therefore, we can write sec x as:

sec x = √(1 + tan² x). This gives us a way to express sec x directly in terms of tan x.