Question

guys plz give that solution prove that
Sinx/1+Cosx = Tanx/2​

Answer 1

Step-by-step explanation:

sinx/1+cos x =tanx/2

LHS=sinx/1+cosx

=2sinx/2 cosx/2/2cos^2x/2

=2sinx/2/2 cos x/2

sinx/2/cosx/2

=tanx/2=RHS

Answer 2

$\bold{\underline{To \ Proof:}}$

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

$\bold{\underline{Proof:}}$

LHS:

$\sf \implies \frac{sin \: x}{1 + cos \: x} \\ \\ \sf sin \: 2x = 2sin \: x.cos \: x \\ \sf sin \: x = 2sin \: \frac{x}{2} .cos \: \frac{x}{2} : \\ \\ \sf \implies \frac{2sin \: \frac{x}{2} .cos \: \frac{x}{2}}{1 + cos \: x} \\ \\ \\ \sf cos \: 2x = 2 {cos}^{2} \: x - 1 \\ \sf cos \: 2x = 2 {cos}^{2} \: \frac{x}{2} - 1 : \\ \\ \sf \implies \frac{2sin \: \frac{x}{2} .cos \: \frac{x}{2}}{1 + 2 {cos}^{2} \: \frac{x}{2} - 1 } \\ \\ \sf \implies \frac{ \cancel{2}sin \: \frac{x}{2} .cos \: \frac{x}{2}}{ \cancel{ 2} {cos}^{2} \: \frac{x}{2} } \\ \\ \sf \implies \frac{sin \: \frac{x}{2} . \cancel{cos \: \frac{x}{2}}}{ cos \: \frac{x}{2}.\cancel{cos \: \frac{x}{2}} } \\ \\ \sf \implies \frac{sin \: \frac{x}{2} }{cos \: \frac{x}{2} } \\ \\ \sf \implies tan \: \frac{x}{2}$

RHS:

$\sf \implies tan \: \frac{x}{2}$

$\therefore$

$\bold{LHS = RHS}$

$\underline{ \sf Hence \: Proved}$