How do you prove tan x csc x cos x = 1?

1 Answer
Mar 5, 2018

Write everything in terms of #sin# and #cos# using these basic identities:

#tanx=sinx/cosx#

#cscx=1/sinx#

Now, rewrite the whole problem:

#LHS=color(red)tanx*color(blue)cscx*color(green)cosx#

#color(white)(LHS)=color(red)(sinx/cosx)*color(blue)(1/sinx)*color(green)(cosx/1)#

#color(white)(LHS)=(color(red)sinx*color(green)cosx)/(color(red)cosx*color(blue)sinx)#

#color(white)(LHS)=(cancelcolor(red)sinx*color(green)cosx)/(color(red)cosx*cancelcolor(blue)sinx)#

#color(white)(LHS)=color(green)cosx/color(red)cosx#

#color(white)(LHS)=cancelcolor(green)cosx/cancelcolor(red)cosx#

#color(white)(LHS)=1#

#color(white)(LHS)=RHS#