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Rina8888 [55]
3 years ago
6

Csc^3x-csc^2x-cscx+1=cot^2x(cscx-1)​

Mathematics
2 answers:
belka [17]3 years ago
5 0

Verify the identity:

csc^3x-csc^2x-cscx+1\qquad =cot^2x(cscx-1)\\\\csc^2x(cscx-1)-1(cscx-1) =\quad \downarrow\\\\(csc^2x-1)(cscx-1)\quad \qquad \ =\quad \downarrow\\\\\bigg(\dfrac{1}{sin^2x}-\dfrac{sin^2x}{sin^2x}\bigg)(cscx-1)\ =\quad \downarrow\\\\\\\bigg(\dfrac{1-sin^2x}{sin^2x}\bigg)(cscx-1)\qquad \ =\quad \downarrow\\\\\\\bigg(\dfrac{cos^2x}{sin^2x}\bigg)(cscx-1)\qquad \qquad =\quad \downarrow\\\\\\cot^2x(cscx-1)\qquad \qquad \qquad =cot^2x(cscx-1)\qquad \checkmark

Svetradugi [14.3K]3 years ago
5 0

Sorry, I messed up. So I changed it.

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