Question

(___)^2=(secx-1)(secx+1) Answer:____

Answer 1

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 2

Answer:  The required answer is tan x.

Step-by-step explanation:  We are given to complete the following trigonometric identity :

$(\_\_\_\_\_)^2=(\sec x-1)(\sec x+1).$

We will be using the following identity from trigonometry to complete the given identity :

$1+\tan^2\theta=\sec^2\theta\\\\\Rightarrow \sec^2\theta-1=\tan^2\theta~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Now, we have

$(\sec x-1)(\sec x+1)\\\\=\sec^2x-1\\\\=\tan^2x~~~~~~~~~~[\textup{from equation (i)}]\\\\=(\tan x)^2.$

Thus, the complete identity is

$(\tan x)^2=(\sec x-1)(\sec x+1).$

Thus, the required answer is tan x.