Question

Write an example of question which uses identity
$cosec {}^{2} \alpha = 1 + {cot}^{2} \alpha$
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Answer 1

Refer to the above attachment.

Answer 2

$\huge{\underline{\red{\mathsf{Answer:-}}}}$

$\large \bf{Question:-}$

Tan²A + Cot²A = Sec²ACosec²A - 2

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$\large \bf{Answer:-}$

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Take L.H.S ,

Tan²A + Cot²A

= (Sec²A - 1) + (Cosec²A - 1)

= Sec²A + Cosec²A - 2

= $\large \bf {{\frac{1}{Cos^{2}A}} \: + \: {\frac{1}{Sin^{2}A}} \: -2}$

= $\large \bf {{\frac{Sin^{2}A \: + \: Cos^{2}A}{Cos^{2}ASin^{2}A}}-2}$

= $\large \bf {{\frac{1}{Cos^{2}ASin^{2}A}}-2}$

= $\large \bf {Sec^{2}A.Cosec^{2}A-2}$

Hence Proved