Question

solve : 1+cosx /sinx=sinx/1+cosx = 2cotx​

Answer 1

★$\bold{\large{\underline{\underline{\rm{\red{Correct\: Question:-}}}}}}$

• prove ((sinx)/(1-cosx)-(sinx)/(1+cosx))=2cotx

★$\bold{\underline{\underline{\large{\rm{\orange{Answer:-}}}}}}$

$\sf \: LHS = \dfrac{(( \sin x)(1 + \cos x) - ( \sin x)(1 - \cos x))}{((1 - \cos x)(1 + \cos x)}$

$\\ \\ \longmapsto \sf \dfrac{( \sin x(1+ \cos x - 1 + \cos x))}{(1 - \cos^2 x)}$

$\\ \\ \longmapsto \sf\dfrac{ \sin x (2 \cos x)}{ \sin^2 x} \: { \red{ \tiny{(since \: \sin^2 x + \cos^2 x = 1,\sin^2 x = 1- \cos^2 x)}}}$

$\\ \\ \longmapsto \sf \: \dfrac{2 \ cos x}{ \sin x}$

$\\ \\ \longmapsto { \large{\boxed{\pink{\sf \: {2 \cot x}}}}}$

$\\ \\ \longmapsto \sf \: RHS$

${ \underline{ \underline{ \blue {\sf {\large{Hence \: Proved.}}}}}}$

Answer 2

Answer:

Step-by-step explanation: