The minimum value of tanθ + cotθ is
(a) 0
(c) -2
(b) 2
(d) 1
WBBSE
Class X
Mathematics
Trigonometric Ratios And Trigonometric Identities
01 Mark
2024
(b) 2
Explanation:
tanθ + cotθ
= (sinθ/cosθ) + (cosθ/sinθ)
= (sin²θ + cos²θ) / (sinθ cosθ)
= 1 / (sinθ cosθ)
Now, we know sin2θ = 2 sinθ cosθ
⇒ sinθ cosθ = (1/2) sin2θ
So, tanθ + cotθ = 1 / (sinθ cosθ) = 2 / sin2θ
The maximum value of sin2θ = 1
So, minimum value of 2 / sin2θ = 2 / 1 = 2
Therefore, minimum value = 2.
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