Question

sin A / 1+cosA + 1+cos A / sin A = 2 cosec A

Answer 1

HOLA

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$\frac{sin}{ \: 1 \: + cos} \: + \: \frac{1 \: + \: cos}{sin} = \: 2 \: cosec \\ \\ \\ \frac{sin}{cos} = \: tan \\ \\ \frac{cos}{sin} = \: cot \\ \\ 1 \: + \: tan \: + \: 1 \: + \: cot \\ \\ tan = \: \frac{1}{cot} = \: cot \\ \\ 1 \: + \: cot \: + \: 1 \: + \: cot \\ \\ 2 \: + \: cot {}^{2} = \: 2cosec \\ \\ here \: we \: have \: used \: 1 \: + \: cot {}^{2}$

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HOPE U UNDERSTAND ❤❤❤

Answer 2

$= > \frac{ \sin(a) }{1 + \cos(a) } + \frac{1 + \cos(a) }{ \sin(a) }$




$\text{Multiply and divide by, }1 - cos(a) \: \: in \: \: \frac{ sin(a) }{1 + \cos(a) }$


$= > \frac{ \sin(a) \times ( 1 - \cos(a) )}{(1 + \cos(a) ) \times (1 - \cos(a)) } + \frac{1 + \cos(a) }{ \sin(a) } \\ \\ \\ \\ = > \frac{ \sin(a)(1 - \cos(a) )}{1 - \cos ^{2} (a) } + \frac{1 + \cos(a) }{ \sin(a) } \\ \\ \\ \\ = > \frac{ \sin(a) - \sin(a) \cos(a) }{ \sin ^{2} (a) } + \frac{1 + \cos(a) }{ \sin(a) } \\ \\ \\ \\ = > \frac{ \sin(a) - \sin(a) \cos(a) + {(1 + \cos(a)) \sin(a) } }{ \sin ^{2} (a) } \\ \\ \\ \\ = > \frac{ \sin(a) - \sin(a) \cos(a) + \sin(a) + \cos (a) \sin(a) }{ \sin^{2} (a) } \\ \\ \\ \\ = > \frac{2 \sin(a) }{ \sin ^{2} (a) } \\ \\ \\ \\ = > \frac{2}{ \sin(a) } \\ \\ \\ \\ 2 cosec(a)$





Hence, proved.