Question

(1-tanA/1-cotA)²= tan²A prove it

Answer 1

Answer:

L.H.S

$(\frac{1 - \tan \: a }{1 - \cot \: a } ) {}^{2}$

$\frac{(1 - tan \: a) {}^{2} }{(1 - cot \: a) {}^{2} }$

$\frac{ (1 - \frac{sin \: a}{cos \: a}) {}^{2} }{(1 - \frac{cos \: a}{sin \: a} ) {}^{2} }$

$\frac{( \frac{cos \: - sin}{cos}) {}^{2} }{( \frac{sin \: - cos}{sin}) {}^{2} }$

$\frac{( \frac{cos {}^{2} + sin {}^{2} - 2cos \: sin }{cos {}^{2} }) }{ \frac{sin {}^{2} + cos {}^{2} - 2sin \: cos }{sin {}^{2} } }$

$\frac{ \frac{1}{cos {}^{2} a} }{ \frac{1}{sin {}^{2}a } }$

$\frac{sin {}^{2}a }{cos {}^{2}a }$

$( \frac{sin \: a}{cos \: a} ) {}^{2}$

$= tan {}^{2} a$

L.HS = R.H.S

hence proved

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