Question

`sec(-x)cos(x)` ?

Use trigonometric identities to simplify the expression

Answer 1

It simplifies to `1`

Explanation:

Given: `sec(-x)cos(x)`

Use the identity `sec(u) = 1/cos(u)` where `u = -x`:

`cos(x)/cos(-x)`

Use the even property of the cosine function `cos(-x) = cos(x)`:

`cos(x)/cos(x)`

Anything divided by itself is 1:

`1`

Answer 2

1

Explanation:

`sec(x)=1/cos(x)`, so `sec(-x)=1/cos(-x)`.

Recall that `cos(x)` is an even function, meaning that `cos(-x)=cos(x)`.

`sec(-x)cos(x)=1/cos(-x) * cos(x) = 1/cancelcos(x) * cancelcos(x)=1`