Question

please answer quickly friends.​

Answer 1

$\huge\mathfrak{\red{solution}}$

To prove:

$\boxed{ \bold{\sqrt{ \frac{1 + cos \theta}{1 - cos \theta} } = cosec \theta + cot \theta}}$

LHS

$\ \sqrt{ \frac{1 + cos \theta}{1 - cos \theta \: } }$

Rationalise the denominator.

$\rightarrow \: \sqrt{ \frac{1 + cos \theta}{ 1 -cos \theta } \times \frac{1 + cos \theta}{1 + cos \theta} } \\ \\ \rightarrow \: \sqrt{ \frac{( 1 + cos \theta) ^{2} }{( {1 - cos^{2} \theta})} } \\ \\ \rightarrow \sqrt{ \frac{ {(1 + cos \theta)}^{2} }{ {sin}^{2 } \theta } } \\ \\ \rightarrow \: \frac{1 + cos \theta}{sin \theta} \\ \\ \rightarrow \: \frac{1}{sin \theta} + \frac{cos \theta}{sin \theta} \\ \\ \rightarrow \: cosec \theta + cot \theta$

LHS = RHS

$\huge\bold{proved}$

Formula used :

$\boxed{ \bold{(x + y)(x - y) = {x}^{2} - {y}^{2} } }$

$\boxed{ \bold{{sin}^{2} \theta + {cos}^{2} \theta = 1}}$

Answer 2

following answer.

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