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Verified Answer :

syed514

 cscx(cos²x - 1) = -sin²x/sinx
                         = - sinx 

Answer:

(-sinx)

Step-by-step explanation:

The given expression is cox²x cosecx - cosecx

We have to simplify it

= cos²x\((\frac{1}{sinx})-(\frac{1}{sinx})\)

= \(\frac{cos^{2}x }{sinx}-\frac{1}{sinx}\)

= \(\frac{1}{sinx}\) × (cos² x-1)

= -\(\frac{1-con^{2}x}{sinx}\)

= -\(\frac{sin^{2}x}{sinx}\)

= - sinx

Therefore, (-sinx) is the answer.

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