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