How do you verify the identity #1/(sinx+1)+1/(cscx+1)=1#?

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Answer 1 · 2017-01-17T18:24:49

see below

Left Hand Side:
#1/(sinx+1) + 1/(cscx +1) =1/(sinx+1) +1/(1/sinx +1)#

#=1/(sinx+1) +1/((1 +sinx)/sinx)#

#=1/(sinx+1) +sin x/(1 +sinx)#

#=1/(1+sinx) +sin x/(1 +sinx)#

#=(1+sinx)/(1+sinx)#

#=cancel(1+sinx)/cancel(1+sinx)#

#=1#

#:.=# Right Hand Side