Question

1-tanA is equal to how much​

Answer 1

SOLUTION

TO DETERMINE

$\displaystyle \sf{ \frac{1 - \tan A}{1 - \cot A} }$

EVALUATION

$\displaystyle \sf{ \frac{1 - \tan A}{1 - \cot A} }$

$\displaystyle \sf{ = \frac{1 - \tan A}{1 - \frac{1}{\tan A} } }$

$\displaystyle \sf{ = \frac{1 - \tan A}{\frac{\tan A - 1}{\tan A} } }$

$\displaystyle \sf{ = \frac{\tan A(1 - \tan A)}{ \tan A - 1} }$

$\displaystyle \sf{ = \frac{ - \tan A(\tan A - 1)}{ \tan A - 1} }$

$\displaystyle \sf{ = - \tan A}$

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