Answer:
tan
Step-by-step explanation:
(secx - 1)(secx + 1)
Remove parentheses = sec²x - 1
Use the identity: tan²x + 1 = sec²x = tan²x + 1 - 1
= tan²x
tan²x = (secx - 1)(secx + 1)
Answer: The required answer is tan x.
Step-by-step explanation: We are given to complete the following trigonometric identity :
[tex](\_\_\_\_\_)^2=(\sec x-1)(\sec x+1).[/tex]
We will be using the following identity from trigonometry to complete the given identity :
[tex]1+\tan^2\theta=\sec^2\theta\\\\\Rightarrow \sec^2\theta-1=\tan^2\theta~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Now, we have
[tex](\sec x-1)(\sec x+1)\\\\=\sec^2x-1\\\\=\tan^2x~~~~~~~~~~[\textup{from equation (i)}]\\\\=(\tan x)^2.[/tex]
Thus, the complete identity is
[tex](\tan x)^2=(\sec x-1)(\sec x+1).[/tex]
Thus, the required answer is tan x.
