tan θ + cot θ = _____?
- sec θ cos θ
- sin θ cosec θ
- sec θ cosec θ
- None of these
Explanation
tan θ = sin θ/cos θ and cot θ = cos θ/sin θ
tan θ + cot θ = sin θ/cos θ + cot θ = cos θ/sin θ
= sin^2 θ + cos^2 θ/sin θ cos θ
= 1/sin θ cos θ (since sin² θ + cos² θ = 1)
Now, 1/sin θ cos θ = 1/sin θ × 1/cos θ = cosec θ × sec θ = sec θ cosec θ
The answer is sec θ cosec θ.
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