How do you verify #tan(x) / (1-cos(x))= csc(x)(1+sec(x))#?

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Answer 1 · 2016-04-17T03:37:24

See below

Left Side #=(tanx/(1-cosx)) xx (1+cosx)/(1+cosx)#

#=(tanx (1+cosx))/((1-cosx)(1+cosx))#

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

=#(tanx (1+cosx))/sin^2x#

=#(((sinx/cosx) (1+cosx))/sin^2x)#

=#((sinx/cosx) (1+cosx))(1/sin^2x)#

=#1/sinx xx (1+cosx)/cosx#

=#cscx (1/cosx +cosx/cosx)#

=#cscx(secx+1)#

=#cscx(1+secx)#

=Right Side