Question 289502
Use the identities.
{{{ tan(x)=sin(x)/cos(x) }}}
{{{cot(x)=cos(x)/sin(x)}}}
{{{sec(x)=1/cos(x)}}}
{{{sec(x)^2=1/cos(x)^2}}}
{{{sin(x)^2+cos(x)^2=1}}}
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{{{tan(x)(cot(x)+tan(x))=tan(x)cot(x)+tan(x)^2}}}
{{{tan(x)(cot(x)+tan(x))=1+sin(x)^2/cos(x)^2}}}
{{{tan(x)(cot(x)+tan(x))=cos(x)^2/cos(x)^2+sin(x)^2/cos(x)^2}}}
{{{tan(x)(cot(x)+tan(x))=(cos(x)^2+sin(x)^2)/cos(x)^2}}}
{{{tan(x)(cot(x)+tan(x))=(1)/cos(x)^2}}}
{{{tan(x)(cot(x)+tan(x))=sec(x)^2}}}