Question

Verify that the equation is an identity sec X - COS X= sin x tan x To verify the identity, start with the more complicatad side and transfom it to look like the other side. Choose the co séc X-COS X COS X Use a common denominator to perform the subtraction. Separate the expression into two factors = sin x tan x

Answer 1

You have the following equation:

secx - cosx = sinxtanx

In order to verify the previous identity, you show that the left side is equal to the right side. You proceed as follow:

secx - cosx = 1/cosx - cosx

to get the same denominators multiply by cosx/cosx in the second term:

1/cosx - cos²x/cosx

add the homogeneus fractions:

(1 - cos²x)/cosx

use the identity sin²x + cos²x = 1 => 1 - cos²x = sin²x

sin²x/cosx

write sin²x as sinxsinx

(sinx)(sinx/cosx)

separate the expression into two factors by replacing sinx/cosx = tanx

(sinx)(tanx)

Then, the given equation is an identity and it has been demonstrated that

secx - cosx = sinx tanx