How do you verify $(tanx/(1+cosx)) + (sinx/(1-cosx))=cotx + secxcscx$ ?

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Answer 1 · 2018-04-20T22:55:38

$LHS=(tanx/(1+cosx)) + (sinx/(1-cosx))$

$=(tanx(1-cosx) + sinx(1+cosx))/(1-cos^2x)$

$=(tanx-tanxcosx + sinx+sinxcosx)/sin^2x$

$=(sinx/cosx-sinx/cosx*cosx + sinx+sinxcosx)/sin^2x$

$=(sinxsecx-cancelsinx +cancel sinx+sinxcosx)/sin^2x$

$=(sinxsecx)/sin^2x +(sinxcosx)/sin^2x$

$=secx/sinx +cosx/sinx$

$=cotx + secxcscx=RHS$

How do you verify (tanx/(1+cosx)) + (sinx/(1-cosx))=cotx + secxcscx(tanx/(1+cosx)) + (sinx/(1-cosx))=cotx + secxcscx?