Simplify the LHS of the identity?

Question

(tan(x)-sin(x)) / (tan(x)sin(x)) = (1-cos(x)) / sin(x))
Simplify the LHS of the equation, please provide all steps THANK YOU! :)

Answer 1

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Answer 2

L.H.S = tan(x)-sin(x)) / (tan(x)sin(x))

= [(sinx/cosx) - sinx] / [(sinx/cosx)sinx]

= [sinx(1 - cosx)/cosx] / [sin²x/cosx]

= { [sinx(1 - cosx)] / [sin²x] } [cosx/cosx]

= {(1 - cosx) / [sinx]} (1) = (1 - cosx) / sinx = RHS

hope this helps

Answer 3

(tanX - sinX) / (tanX.sinX) ...... divide top & bottom by tanX

= (1 - sinX / tanX) / tanX ........ simplify sinX / tan X

= (1 - cosX ) / sinX

QED