4. cosec x (sec x - 1) - cot x (1 - cos x) = tan x - sinx
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Answer:
LHS = 1/sin x(1/cos x-1) - cos x/sinx (1-cos x)
=1-cos x/sin xcos x -( 1-cosx) cosx/sinx
=(1-cosx/sinx)[1/cosx - cosx]
=(1-cosx/sinx)sin*2x/cosx
=(1-cosx)sinx/cosx
=sinx/cosx -sinx
=tanx-sinx=RHS
HENCE LHS=RHS
proved
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