Question 916596
{{{sin(x)(csc(x)+sin(x)*sec^2(x))=sec^2(x)}}}

{{{highlight(sin(x)(csc(x)+sin(x)*sec^2(x)))}}} ....prove it's equal to right side


we know that {{{csc(x)=1/sin(x)}}}

then we have

={{{sinx(1/sin(x) +sinx*sec^2 (x))}}}


={{{sinx(1/sin(x) +(sin(x)*sin(x)*sec^2(x))/sin(x))}}}


={{{sin(x)(1/sin(x) +(sin^2(x)*sec^2(x))/sin(x))}}}



={{{cross(sin(x))(1/cross(sin(x))1 +(sin^2(x)*sec^2(x))/cross(sin(x)))}}}


={{{1+sin^2(x)*sec^2(x)}}}......{{{sin^2(x)*sec^2(x)=tan^2(x)}}}


={{{1+tan^2(x)}}} ....use Pythagorean Identities =>{{{1+tan^2(x)=sec^2(x)}}}


={{{highlight(sec^2(x) )}}}