Question

write tan x in terms of sec x. a. tan x = ±√(sec²x - 1) b. tan x = (±sec x√(sec²x - 1))/(sec²x - 1) c. tan x = (±√(sec²x - 1))/(sec²x - 1) d. tan x = (±√(sec²x - 1))/sec x

Explanation:

Step1: Recall trigonometric identity

We know the Pythagorean identity $\tan^{2}x + 1=\sec^{2}x$.

Step2: Isolate $\tan^{2}x$

Subtract 1 from both sides of the identity: $\tan^{2}x=\sec^{2}x - 1$.

Step3: Solve for $\tan x$

Take the square - root of both sides: $\tan x=\pm\sqrt{\sec^{2}x - 1}$.

Answer:

A. $\tan x=\pm\sqrt{\sec^{2}x - 1}$