Question

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

Answer 1

`\cos t \, (\sec t - \cos t)`

`= \cos t \, ((1)/(\cos t) - \cos t)`

`= 1 - \cos^2 t`

`= \bf sin^2 t`

Answer 2

sin^2(t)

Explanation:

cos t(sec t − cos t)

To simplify this we use trigonometri identities

`sec(x)= (1)/(cosx)`

Replace sec t with 1/cos(t)

`cos(t)((1)/(cos(t))-cos(t))`

Distribute cos(t) inside the parenthesis

`(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)