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

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