Explanation

Expand: (1+tanαtanβ)² + (tanα−tanβ)² = 1 + 2tanαtanβ + tan²αtan²β + tan²α − 2tanαtanβ + tan²β. The cross terms cancel, leaving 1 + tan²α + tan²β + tan²αtan²β = (1+tan²α)(1+tan²β). Since 1+tan² = sec², this equals sec²αsec²β — option B.