Question

Value of tan(90 - cot^-1(1/3))

Answer 1

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Answer 2

SOLUTION

TO DETERMINE

The value of

$\displaystyle \sf{ tan \bigg( {90}^{ \circ} - {cot}^{ - 1} \bigg( \frac{1}{3} \bigg) \bigg) }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula

$\displaystyle \sf{1. \: \: tan ( {90}^{ \circ} - \theta) = cot \theta}$

$\displaystyle \sf{ 2. \: \: cot ( {cot}^{ - 1} x ) } = x$

EVALUATION

Here it is given that

$\displaystyle \sf{ tan \bigg( {90}^{ \circ} - {cot}^{ - 1} \bigg( \frac{1}{3} \bigg) \bigg) }$

We simplify it as below

$\displaystyle \sf{ tan \bigg( {90}^{ \circ} - {cot}^{ - 1} \bigg( \frac{1}{3} \bigg) \bigg) }$

$\displaystyle \sf{ = cot \bigg( {cot}^{ - 1} \bigg( \frac{1}{3} \bigg) \bigg) } \: \: \: : Using \: Formula \: 1$

$\displaystyle \sf{ = \frac{1}{3} } \: \: \: : Using \: Formula \: 2$

FINAL ANSWER

$\displaystyle \sf{ tan \bigg( {90}^{ \circ} - {cot}^{ - 1} \bigg( \frac{1}{3} \bigg) \bigg) = \frac{1}{3} }$

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