Question

Prove that 1-cosx/sinx = tan x/2 = sinx/1+cosx

Answer 1

Answer:

• 1-cosx/sinx

Step-by-step explanation:

• 1-cosx=1-(1-2sin*2x/2)
• " " =2sin*2x/2
• and sinx=2sinx/2×cosx/2
• putting values
• you will get the required result and proceed same from other side

Answer 2

$\Large\underline\blue{\bold{To \: Prove :}}$

• $\tt \: tan\dfrac{x}{2} = \dfrac{sinx}{1 + cosx}$

$\Large{\bold{\underline{\blue{Formula \: Used :}}}}$

$\longmapsto\: \:\boxed{\red{\bf\:sin2x = 2sinx \: cosx }}$

$\longmapsto \: \:\boxed{\red{\bf\: 1 + cos2x = 2 {cos}^{2} x}}$

$\Large\underline{\purple{\bold{Solution : }}}$

$\bf \: Consider \: RHS$

$\rm :\implies\:\dfrac{sinx}{1 + cosx}$

$\rm :\implies\:\dfrac{2 \: sin\dfrac{x}{2} \: cos\dfrac{x}{2} }{2 {cos}^{2} \dfrac{x}{2} }$

$\rm :\implies\:\dfrac{sin\dfrac{x}{2} }{cos\dfrac{x}{2} }$

$\rm :\implies\:tan\dfrac{x}{2}$

$\rm :\implies\: = \: LHS$

$\large{\boxed{\boxed{\bf{Hence, Proved}}}}$