The minimum value of tan B tanC in an acute angled triangle ABC is-
Question
The minimum value of tan B tanC in an acute angled triangle ABC is-
Solution
In an acute angled triangle ABC, the sum of two angles is always less than 180 degrees.
Let's consider two angles B and C.
According to the trigonometric identity, tan(B) * tan(C) = tan(B) * tan(180 - B) = tan(B) / tan(B) = 1 (since tan(180 - θ) = -tan(θ) for any angle θ).
So, the minimum value of tan(B) * tan(C) in an acute angled triangle ABC is 1.
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