Question

Prove that (cosec theta - cot theta)^ 2 =
1- cos theta / 1+ cos theta ..

Answer 1

first write L.H.S and then solve it

Answer 2

Step-by-step explanation:

$\huge{\pink{\boxed{\green{\underline{\red{\sf{SOLUTION-}}}}}}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: { \orange{to \: prove}} \\ {\pink{ \boxed{ \red{(cosec \theta - cot \theta)^{2} = \frac{1 - cos \theta}{1 + cos \theta} }}}}$

☆ Use some trigonometric identites to proof:

$\to(cosec \theta - cot \theta)^{2} = \frac{1 - cos \theta}{1 + cos \theta} \\ \: \: \: \: \: \: \: \: \: \: \: </strong><strong>L</strong><strong>H</strong><strong>S</strong><strong> \\ \to(cosec \theta - cot \theta)^{2} \\ \to ( \frac{1}{sin \theta} - \frac{cos \theta}{sin \theta} ) ^{2} \\ \to( \frac{1 - cos \theta}{sin \theta} )^{2} \\ \to \frac{(1 - cos \theta) ^{2} }{sin^{2} \theta } \\ \to \frac{(1 - cos \theta)^{2} }{ {1}^{2} - cos^{2} \theta } \\ \to \frac{(1 - cos \theta)(1 - cos \theta)}{(1 + cos \theta)(1 - cos \theta)} \\ \to \frac{1 - cos \theta}{1 + cos \theta}$

$\huge{\pink{\boxed{\green{\underline{\sf{RHS\:PROVED-}}}}}}$

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