`1/sin(x) - 1/csc(x) = csc(x) - sin(x)` Verfiy the identity.

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mathace eNotes educator| Certified Educator

Verify the identity: `1/sin(x)-1/csc(x)=csc(x)-sin(x)`

Simplify the left side of the equation using the following reciprocal identities:

1/sin(x)=csc(x)  and 1/csc(x)=sin(x).

`csc(x)-sin(x)=csc(x)-sin(x)` 

balajia | Student

We know that `sinx = 1/cscx.` Using this result ,

By cross multiplication we get 

`1/sinx-1/cscx = (cscx-sinx)/(sinx.cscx) = cscx-sinx.`  Since  `sinx = 1/cscx.`