Question

Prove
that. (Cosec O - cotO)² =
1-cosO/1+cosO. - prove that cosec theta minus cot theta whole square is equal to 1 minus cos theta by 1 + cos theta ​

Answer 1

Answer:

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Answer 2

$\huge\mathbb{QUESTION \to: }$

$\small\mathbb{TO \: PROVE \mapsto: {(cosec \theta \: - cot \theta)}^{2} = \frac{1 - cos \theta}{1 + cos \theta} }$

$\huge\mathbb{SOLUTION \leadsto: }$

$\bf\ using \: formula \: \\ \sf\ {sin}^{2} \theta + {cos}^{2} \theta = 1 \\ \sf\ \implies \boxed{ {sin}^{2} \theta }= 1 - {cos}^{2} \theta \\ \\ \\ \bf\ {(cosec \theta - cot \theta)}^{2} \\ \\ \bf\ \mapsto: {( \frac{1}{sin \theta} - \frac{cos \theta}{sin \theta} )}^{2} \\ \\\bf\ \mapsto: {( \frac{1 - cos \theta}{sin \theta} )}^{2} \\ \\\bf\ \mapsto: \frac{ {(1 - cos \theta)}^{2} }{ {sin}^{2} \theta} \\ \\ \bf\ \mapsto: \frac{ {(1 - cos \theta)}^{2} }{1 - {cos}^{2} \theta} \\ \\ \bf\ \mapsto: \frac{(1 - cos \theta)(1 - cos \theta)}{ {1}^{2} - {cos}^{2} \theta} \\ \\ \bf\ \mapsto: \frac {(1 - cos \theta) \cancel{(1 - cos \theta)}}{(1 + cos \theta) \cancel{(1 - cos \theta)}} \\ \\ \bf\boxed{ \mapsto: \frac{(1 - cos \theta)}{(1 + cos \theta)} }$