Question
Simplifies- (1 + tan²A) + (1+ 1 /tan²A)
[A] 1/ (sin²A-sin4 A) [C] 1/ (cos2 A-sin4 A) [B] 1/ (sin²A-cos4 A) [D]1/ (cot2 A-tan4 A)Solution
(1+ tan² A) + (1+1/ tan²A) First, we know that: 1 + tan² A= sec² A Also, for the second term: 1+1/ tan² A = 1 + cot² A = csc²A Now, adding these two expressions: sec² A + csc² A =(sin2A+cos2A)/Sin2A.cos2A =1/ ( Sin2A.cos2A) = 1/ (Sin2A (1- Sin2A) =1/ (Sin2A- Sin4A).
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