The minimum value of sin²θ + cos²θ

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The minimum value of sin²θ + cos²θ + sec²θ + cosec²θ + tan²θ + cot²θ is

1. 1
2. 3
3. 5
4. 7

Correct Option: D

sin²θ + cos²θ + sec²θ + cosec²θ + tan²θ + cot²θ
= 1 + sec²θ – tan²θ + cosec²θ – cot²θ + 2(tan²θ + cot²θ )
= 3 + 2 ((tanθ – cotθ) ² + 2) > 7
[(tanθ – cotθ) ² > 0]