Question

help prove that (sinx cotx+cosx)/2cotx=sinx ??

Answer 1

write cot = cos /sin
then simplify

Answer 2

thank you so much!

Answer 3

sinx cosx/sinx+cosx=2cosx

2cosx/2cosx/sinx=sinx

Answer 4

See. There are many ways to solve it.
1. take the primary formulae for every trigonometric identities. i.e. sinx=p/h, cotx=b/p cosx=b/h and all that then you may sove it. but its a li'l bit leanthy.
2. given (sinx.cotx+cosx)/2cotx =LHS
put cotx=cosx/sonx
so , (sinx(cosx/sinx)+cosx)/2cotx
= (cosx+cosx)/2cotx
=2cosx/2cotx
=cosx/(cosx/sinx)
=sinx =RHS
; hance proved :)

Answer 5

\[\frac{ \sin x \cot x +\cos x }{ 2\cot x}=\frac{ \sin x \frac{ \cos x }{ } +\cos x }{ 2\frac{ \cos x }{ \sin x }}=\\ \frac{ 2\cos x }{ \ }/\frac{ 2\cos x }{ \sin x }\]