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#