If tan θ + cotθ = 5, and θ is an acute angle, find the value of tan²θ + cot²θ.
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Correct answer: D
Explanation
given :
tanθ + cotθ = 5
According to the formula:
(tanθ + cotθ)² = tan²θ + cot²θ + 2
(tanθ + cotθ)² = 5²
25 = tan²θ + cot²θ + 2
tan²θ + cot²θ = 25 − 2
tan²θ + cot²θ = 23