Question

Simplify this expression: cos t(sec t − cos t)

Answer 1

Answer:

sin^2(t)

Step-by-step explanation:

cos t(sec t − cos t)

To simplify this we use trigonometri identities

$sec(x)= \frac{1}{cosx}$

Replace sec t with 1/cos(t)

$cos(t)(\frac{1}{cos(t)}-cos(t))$

Distribute cos(t) inside the parenthesis

$\frac{cos(t)}{cos(t)}-cos(t)*cos(t))$

1- cos^2(t)

We know sin^2(x) + cos^2(x)= 1

so 1-cs^2(t)= sin^2(t)

Answer 2

$\cos t \, (\sec t - \cos t)$
$= \cos t \, (\frac{1}{\cos t} - \cos t)$
$= 1 - \cos^2 t$
$= \bf sin^2 t$