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

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Answer 1 · 2015-04-16T09:50:47

We know that #color(blue)(csc x = 1/sinx#

Therefore
#(1/(sinx+1))+(1/(cscx+1)) #

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

Multiplying the Numerator and the Denominator of the second term with #sinx#, we get

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

As the Denominators are the same, we can simply add the numerators over the common denominator

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

# = 1# (which is the Right Hand Side)

Hence Proved.