Question

prove it

$\frac{sin \: a}{1 + cos \: a} = \frac{tan \: a}{2}$

Answer 1

Answer:

Step-by-step explanation:

LHS=sin a / 1+cosa

Divide both part by cos,

=tan a / 1+1

=tan a / 2

Answer 2

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$\bold{Dear\:user!!}$



$\bold{\underline{Question-}}$

prove it

$\frac{sin \: a}{1 + cos \: a} = \frac{tan \: a}{2}$




$\bold{\underline{Answer-}}$

LHS = $\frac{sin \: a}{1 + cos \: a}$

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


$= \frac{2 \sin \frac{1}{2}a \: \cos \frac{1}{2}a}{2 { \cos}^{2} \frac{1}{2}a }$


$= \frac{ \sin \frac{1}{2}a }{ \cos \frac{1}{2} a}$


$= \tan \frac{1}{2} a$



LHS = RHS

Hence proved,