tanθ + cotθ = ______?
- cosecθ
- secθ
- secθcosecθ
- None of these
Explanation
Let's simplify the expression:
tanθ + cotθ
= sinθ/cosθ + cosθ/sinθ
= (sin²θ + cos²θ) / (sinθcosθ)
Since sin²θ + cos²θ = 1:
= 1 / (sinθcosθ)
= 1/sinθ * 1/cosθ
= cosecθ * secθ
= secθcosecθ
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