Question

SinA(1+tanA)+cosA(1+cotA)=CosecA+SecA​

Answer 1

Hope it is helpful ☺☺

Answer 2

$\huge\sf{Answer}$

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

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

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

=>$\frac{ { \sin(a) }^{2} + { \cos(a) }^{2} }{ \sin(a) \cos(a) } + \sin(a) + \cos(a)$

=>$we \: know \: that \: { \ { \sin(a) }^{2} + { \cos(a) }^{2} } = 0$

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

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

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

=>$\sec(a) + \csc(a)$

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