How do you verify #sec^2 x/ tan x = sec x csc x#?

Question

5074 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-31T08:28:10

By using the following rules :
#secx=1/cosx#

#cscx=1/sinx#

#tanx=sinx/cosx#

Required to prove : #sec^2x/tanx= secxcscx#

Starting from the Left Hand Side of the equation

#"LHS"=sec^2x/tanx#

#=(secx)^2/tanx#

#=(1/cosx)^2/(sinx/cosx)#

#=1/(cosx)^2÷(sinx/cosx)#

#=1/(cosx)^cancel2*cancelcosx/sinx#

#=1/cosx*1/sinx#

#=color(blue)(secxcscx#

#"QED"#