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

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Answer 1 · 2016-11-17T19:42:29

see below

$(1+tanx)/(sinx+cosx)=secx$

Left Side: $=(1+tanx)/(sinx+cosx)$

$=(1+sinx/cosx)/(sinx+cosx)$

$=((cosx+sinx)/cosx)/(sinx+cosx)$

$=(cosx+sinx)/cosx*1/(sinx+cosx)$

$=(sinx+cosx)/cosx*1/(sinx+cosx)$

$=cancel(sinx+cosx)/cosx*1/cancel(sinx+cosx)$

$=1/cosx$

$=sec x$

$:.=$ Right Side

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