In an acute angled triangle abc , the minimum value of tan a*tanb*tanc is
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THE MINIMUM VALUE IS
TAN 60° * TAN 60° * TAN 60°
= √3 * √3 * √3
= 3 √3
= 3 * 1.732
= 5.196.
TAN 60° * TAN 60° * TAN 60°
= √3 * √3 * √3
= 3 √3
= 3 * 1.732
= 5.196.
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Given:
an acute angled triangle abc.
To find:
minimum value of tan a*tanb*tanc.
Solution:
1) It is given in the question that the given triangle is acute angled triangle so to make the given expression minimum there is only one triangle is possible whose all angles are 60°.
2) So the minimum value of the expression:
- tan60° × tan60° × tan60°
- √3 × √3 ×√3
- 3√3
- 3 × 1.732
- 5.196
minimum value of tan a*tanb*tanc is 5.196.
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