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

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

3 Answers
Mar 11, 2018

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

Mar 11, 2018

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

Mar 11, 2018

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