Question

How do you work out: (tan(x)cos(x))/(sin(x))?

Can someone explain how to work out: (tan(x)cos(x))/(sin(x))

Answer 1

The equation is equal to `1`.

Explanation:

Use this trig identity to simplify the expression:

`tanx=sinx/cosx`

Here's the problem:

`color(white)=(color(blue)(tanx)*cosx)/sinx`

`=(color(blue)sinx/color(blue)cosx*cosx)/sinx`

`=(color(blue)sinx/color(red)cancelcolor(blue)cosx*color(red)cancelcolor(black)cosx)/sinx`

`=color(blue)sinx/sinx`

`=1`

Answer 2

1

Explanation:

Step by step:
`tanx*cosx/sinx`
A quotient identity states:
`cosx/sinx= cotx`
Therefore:
`tanx*(cotx)`
A reciprocal identity states:
`cotx=1/tanx`
Therefore substitute `1/tanx` for `cotx`:
`cancel(tanx)*1/cancel(tanx)=`
`1`

Answer 3

1

Explanation:

`(tan(x) cos(x))/sin(x)`

`= tan(x) xx cos(x)/sin(x)`

`= tan(x) xx 1 / (sin(x)/cos(x))`

`= tan(x) xx 1/tan(x)`

`= tan(x)/tan(x)`

`= 1`