If cos A = 4/5 and A is acute, then find the value of (1 + tan² A) / (1 + cot² A).
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Correct answer: C
Explanation
Given:
cos A = 4/5, where A is an acute angle.
According to the formulas:
1 + tan²A = sec²A
1 + cot²A = cosec²A
(1 + tan²A) / (1 + cot²A) = sec²A / cosec²A
sec²A / cosec²A = (1/cos²A) / (1/sin²A)
= sin²A / cos²A
= tan²A
cos A = 4/5
sin A = 3/5
tan A = sin A / cos A
= (3/5) / (4/5)
= 3/4
tan²A = (3/4)² = 9/16