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.

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