8. (sec A sec B + tan A tan B)2 – (sec A tan B + tan A sec B)2 = 1
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Step-by-step explanation:
(sec A sec B + tan A tan B)²– (sec A tan B + tan A sec B)²
=(sec A sec B)²+(tan A tanB)²+2 sec A.sec B.tan A.tan B–(sec A tanB)²–(tan A sec B)²–2 sec A.sec B.tan A.tan B
=sec²A(sec²B-tan²B)–tan²A(sec²B-tan²B)
=(sec²B-tan²B)(sec²A-tan²A)
=1
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