Question

tan 1/2 (x) = sin(x)/ 1+cos(x)

Answer 1

Step-by-step explanation:

$tan \frac{x}{2} = \frac{sinx}{1 + cosx} \\ \: \: \: \: \: \: \: \: = \frac{2sin \frac{x}{2} cos \frac{x}{2} }{1 + 2 {cos}^{2} \frac{x}{2} - 1 }\\ = tan \frac{x}{2} \\ \\ Hope \: it \: will \: hep \: you \:$

Answer 2

Answer:

Step-by-step explanation:

tan 1/2 (x) = sin(x)/ 1+cos(x)

RHS=sin(x)/ 1+cos(x)

=2sin(x/2)cos(x/2)/(1+cos²x/2-sin²x/2)

= 2sin(x/2)cos(x/2) /( sin²x/2+cos²x/2+cos²x/2-sin²x/2)

=2sin(x/2)cos(x/2) / 2cos²x/2

= sin(x/2)/cos(x/2)

= tan (x/2) =LHS