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Question
Select the correct option from the given alternatives :
In ∆ABC if cot A cot B cot C > 0 then the triangle is _________
Options
Acute angled
right angled
obtuse angled
isosceles right angled
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Solution
Acute angled
Explanation:
cot A cot B cot C > 0
- Case I:
cot A, cot B, cot C > 0
∴ cot A > 0, cot B > 0, cot C > 0
∴ 0 < A < `pi/2`, 0 < B < `pi/2`, 0 < C < `pi/2`
∴ ΔABC is an acute angled triangle. - Case II:
Two of cot A, cot B, cot C < 0
0 < A, B, C < π and
two of cot A, cot B, cot C < 0
∴ Two of angles A, B, C are in 2nd quadrant which is not possible.
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