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#