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

Textbook Question

Chapter 5, 5.2 - Problem 28 - Precalculus (3rd Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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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)` 

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balajia | College Teacher | (Level 1) eNoter

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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.`

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