Complete the following identity secx-1/secx=? I have four multiple choice options and can't seem to work my way to either one. A) secx cscx B)1+cotx C)sinx tanx D)-2tan^2x
Is the numerator of the fraction 1 or (secx -1)?
secx - (1/secx) = sec x - cos x
= [1 - cos^2x]/cos x
= sin^2x/cosx
= tanx*sinx
The choice is C
Its Answer is secx-cosx
To complete the given identity secx-1/secx, we need to manipulate the expression to bring it to a form where we can apply trigonometric identities.
Let's start by simplifying the expression:
secx - 1/secx
We know that secx is equal to 1/cosx, so we can substitute it:
1/cosx - 1/(1/cosx)
Now, we need to find a common denominator for the fractions. The least common denominator (LCD) is cosx, so we can rewrite the expression with the common denominator:
(1 - cosx)/cosx
Now, let's look at the given options:
A) secx cscx
B) 1+cotx
C) sinx tanx
D) -2tan^2x
Option A is secx multiplied by cscx, which is equivalent to 1 (since secx is the reciprocal of cosx and cscx is the reciprocal of sinx).
Option B is 1 added to cotx, which cannot be simplified to the current expression (1 - cosx)/cosx.
Option C is sinx multiplied by tanx, which is not equivalent to the current expression.
Option D is -2 multiplied by tan^2x, which is not equivalent to the current expression.
None of the given options are equivalent to the expression (1 - cosx)/cosx. Therefore, none of the provided options is the correct answer.
To summarize, the given identity secx-1/secx simplifies to (1 - cosx)/cosx, and none of the given options A, B, C, or D are equivalent to this expression.