How do you verify $(1+tanx)/(sinx)=cscx+secx$ ?

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Answer 1 · 2015-07-28T11:45:16

Use the following rules :
$tanx=sinx/cosx$
$1/sinx=cscx$
$1/cosx=secx$

Start from the Left hand side $("LHS")$ :

$=>"LHS"=(1+tanx)/sinx=1/sinx+tanx/sinx$
$=cscx+tanx xx1/sinx=cscx+cancel(sinx)/cosx xx1/cancel(sinx)=cscx+1/cosx=color(blue)(cscx+secx)$

$QED$

How do you verify (1+tanx)/(sinx)=cscx+secx(1+tanx)/(sinx)=cscx+secx?