simplify sec(x)*cos(-x)-sin(x)^2 with trig identities

[jwpaine]

Simplify \(\displaystyle \L Sec(x)\cdot cos(-x)-Sin(x)^{2}\)

\(\displaystyle \L Sec(x) = \frac{1}{Cos(x)}\) So...

\(\displaystyle \L \frac{1}{Cos(x)}\cdot\frac{Cos(-x)}{1}-1+Cos(x)^{2}\)

And then the Cos(x) over Cos(-x) give me 1... so

\(\displaystyle \L 1 - 1 + Cos(x)^{2}\)

= \(\displaystyle \L Cos(x)^{2}\)

Is this correct? If not...where did I go wrong?

 

[pka]

Yes, that is correct.

 

[jwpaine]

Sweet. Thank you for looking it over.

 

[jwpaine]

Hmmm...

When I enter \(\displaystyle \L cos^{-1}(0.5)\cdot cos(-0.5)-sin(0.5)^{2}\) into my calculator I don't get the same answer as when I do cos(0.5)^2

So..it doesn't seem like this is it's simplification.....even thought the identities are correct.

 

[pka]

Hmmm...

When I enter \(\displaystyle \L cos^{-1}(0.5)\cdot cos(-0.5)-sin(0.5)^{2}\) into my calculator I don't get the same answer as when I do cos(0.5)^2

So..it doesn't seem like this is it's simplification.....even thought the identities are correct.

You calculator is reading \(\displaystyle \L cos^{-1}(0.5)\) as arccosine.
Try \(\displaystyle \L \{{cos(0.5)}\}^{-1}\).