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Solution
$$(\cosec A - \sin A)^2 + (\sec A - \cos A)^2 - (\cot A - \tan A)^2$$
$$= cosec^2A+sin^2A-2cosecAsinA + sec^2A+cos^2A-2secAcosA - (cot^2A+tan^2A-2cotAtanA)$$
$$= cosec^2A+sin^2A-2+sec^2A+cos^2A-2-cot^2A-tan^2A+2$$
$$= (cosec^2A-cot^2A)+(sin^2A+cos^2A)+(sec^2A-tan^2A)-2$$
$$= 3-2 = 1$$
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