Question

Find the principal value of cot^–1 $open parentheses negative fraction numerator 1 over denominator square root of 3 end fraction close parentheses$

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Solution

Let space straight y equals space c o t to the power of negative 1 end exponent open parentheses negative fraction numerator 1 over denominator square root of 3 end fraction close parentheses space where space 0 less than y less than straight pi therefore space space space cot space straight y space equals space minus fraction numerator 1 over denominator square root of 3 end fraction space where space 0 less than straight y less than straight pi therefore space space space cot space straight y space equals space minus space cot straight pi over 3 equals cot open parentheses straight pi minus straight pi over 3 close parentheses equals cot fraction numerator 2 straight pi over denominator 3 end fraction space where space 0 less than straight y less than straight pi therefore space space space space space straight y equals fraction numerator 2 straight pi over denominator 3 end fraction

therefore space space space

required principal value =

fraction numerator 2 straight pi over denominator 3 end fraction.

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