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Verify the identity.

cot^2x/ cscx-1 = 1+sinx/sinx

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cot²x /(cscx + 1) = (1 - sinx) /sinx

let's apply the identity cot²x = csc²x - 1:

(csc²x - 1) /(cscx + 1) = (1 - sinx) /sinx

(factoring csc²x - 1 as a difference of squares and then simplifying)

[(cscx + 1)(cscx - 1)] /(cscx + 1) = (1 - sinx) /sinx

cscx - 1 = (1 - sinx) /sinx

let's recall that cscx = 1 /sinx:

(1 /sinx) - 1 = (1 - sinx) /sinx

ending with:


(1 - sinx) /sinx = (1 - sinx) /sinx (verified)


I hope it helps
User Adam Boddington
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8.3k points

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