Question 982954
Use their definitions and then apply fraction skills and other number property skills.


{{{(1/sin(x)-cos(x)/sin(x))(1/cos(x)+1)}}}


{{{((1-cos(x))/sin(x))(1/cos(x)+cos(x)/cos(x)}}}


{{{((1-cos(x))/sin(x))((1+cos(x))/cos(x))}}}


{{{((1-cos(x))/(1+cos(x)))*cot(x)}}}.........


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*********************Maybe another approach**********************:



Perform the initially indicated multiplication.


{{{csc(x)*sec(x)+csc(x)-cot(x)sec(c)-cot(x)}}}


{{{1/(sin(x)cos(x))+1/sin(x)-(cos(x)/sin(x))(1/cos(x))-cos(x)/sin(x)}}}


{{{(1-cos(x))/(sin(x)cos(x))+(1-cos(x))/sin(x)}}}

Still want to have all same denominator,... be  sin(x)cos(x)...

{{{(1-cos(x))/(sin(x)cos(x))+((1-cos(x))/sin(x))(cos(x)/cos(x))}}}


{{{(1-cos(x))/(sin(x)cos(x))+((1-cos(x))cos(x))/(sin(x)cos(x))}}}


{{{(1-cos(x)+cos(x)-cos^2(x))/(sin(x)cos(x))}}}


{{{(1-cos^2(x))/(sin(x)cos(x))}}}


{{{sin^2(x)/(sin(x)cos(x))}}}


{{{(sin(x)/sin(x))(sin(x)/cos(x))}}}
{{{1*tan(x)}}}


{{{highlight(tan(x))}}}