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

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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

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

$=(secx)^2/tanx$

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

$=1/(cosx)^2÷(sinx/cosx)$

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

$=1/cosx*1/sinx$

$=color(blue)(secxcscx$

$"QED"$

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