Question

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Answer 1

Answer:

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Answer 2

$\frac{1 - tan {}^{2} \alpha }{cot {}^{2} \alpha - 1} = tan {}^{2} \alpha$

LHS:-

$\frac{1 - tan {}^{2} \alpha }{ \frac{1}{tan {}^{2} \alpha } - 1}$

$\frac{1 - tan {}^{2} \alpha }{ \frac{1 - tan {}^{2} \alpha }{tan { }^{2} \alpha } } = \frac{1 - tan {}^{2} \alpha }{1} \times \frac{tan {}^{2} \alpha }{1 - tan {}^{2} \alpha }$

which is equal to ,$tan {}^{2} \alpha$=RHS

Identity used:-

cot²∅ = 1/tan²∅

Cheers!