Question 1207649

given:

{{{(sin (theta )+tan (theta ))/(csc (theta )+cot (theta )) = sin(theta ) tan (theta )}}}

manipulate left side


{{{(sin (theta )+tan (theta ))/(csc (theta )+cot (theta )) }}}...use identities


={{{(sin (theta )+sin (theta )/cos (theta ))/(1/sin (theta ) +cos (theta )/sin (theta )) }}}


={{{((sin (theta )cos (theta )+sin (theta ))/cos (theta ))/((1+cos (theta ))/sin (theta )) }}}


={{{(sin (theta )(cos (theta )+1)/cos (theta ))/((1+cos (theta ))/sin (theta ))}}} ...simplify


={{{(sin (theta )/cos (theta ))/(1/sin (theta ))}}}


={{{sin (theta )(sin (theta )/cos (theta ))}}}


={{{sin (theta )*tan(theta )}}}=< proven