If in a triangle ABC, angles A and B are complementary, then the value of cot C is ________.

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Solution

It is given that angles A and B are complementary.

$∴ A + B = 90 °$ .....(1)

In ∆ABC,

$A + B + C = 180 °$ (Angle sum property of a triangle)

$\Rightarrow 90 ° + C = 180 ° [Using (1)] \Rightarrow C = 180 ° - 90 ° = 90 ° ∴ \cot C = \cot 90 ° = 0$

If in a triangle ABC, angles A and B are complementary, then the value of cot C is 0.

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