Prove That
sin x - cos x +1/sin x + cos X-1
=sec x + tan x.
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('^' = exponent, '*' = multiplication)
LHS = (sin x - cos x +1) / (sin x + cos X-1)
= [(sin x - cos x +1)/(sin x + cos X-1)] * [(sin x - cos x +1)/(sin x - cos X+1)]
=(sin^2 x + 1 +2sinx -cos^2 x) / sin^2 x + cos^2 x + 2sinxcosx - 1
=(2sin^2 x + 2sinx) / (2sinxcosx)
=[2sinx(sin x + 1)] / [2sinxcosx]
=(sinx + 1) / cosx
=sinx/cosx + 1/cosx
=tanx + secx = RHS
Hence proved.
ask me if you have any doubt :)
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