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

Question

4474 views around the world

You can reuse this answer
Creative Commons License

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

How do you verify the identity 1/(sinx+1)+1/(cscx+1)=11/(sinx+1)+1/(cscx+1)=1?