If 0° < A < 90°, then the value of tan²A + cot²

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If 0° < A < 90°, then the value of tan²A + cot² A – sec² A cosec² A is

1. 0
2. 1
3. 2
4. – 2

Correct Option: D

tan²A + cot²A – sec²A . cosec²A
= tan²A + cot²A – (1 + tan²A) (1 + cot²A)
= tan²A + cot²A – (1 + tan²A +
cot²A + cot²A.tan²A)
= tan²A + cot²A – 1 – tan²A – cot²A – cot²A . tan²A
= – 1 – 1 = – 2
[ tanA . cotA = 1]