Question

(1- COtA/1- tanA)=cot^2

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Answer 1

QUESTION

PROVE THAT

$\dfrac{1 - cot \: a}{1 - tan \: a} = - {cot} a$

ANSWER

LHS

$\dfrac{1 - cot \: a}{1 - tan \: a} \\ \\ = \frac{1 - cot \: a}{1 - \frac{1}{cot \: a} } \\ \\ = \dfrac{( - )(cot \: a - 1)}{ \dfrac{cot \: a - 1}{cot \: a} } \\ \\ = - cot \: a$

RHS

(-cot a)

HENCE LHS =RHS

(PROVED)