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$$\cot^2A+\cos^2A=\operatorname{cosec}^2A-1+1-\sin^2A$$
$$=$$> $$\cot^2A+\cos^2A=\operatorname{cosec}^2A-\sin^2A$$
$$=$$> $$\cot^2A+\cos^2A=\left(\operatorname{cosec}A+\sin A\right)\left(\operatorname{cosec}A-\sin A\right)$$
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