Question

cos(90-a)sin(90-a)/tan(90-a)=sin^2a

Answer 1

lhs→
=[sin(a)cos(a)]/cot(a)
=sin(a)cos(a)×sin(a)/cos(a). [ cot(a)= cos(a)/sin(a) ]
=sin(a)sin(a) [cancelling cos(a)/cos(a)]
=sin^2 (a).
hence proved

Answer 2

cos(90-a)=sin(a)
sin(90-a)=cos(a)
tan(90-a)=cot(a)
:. sin(a).cos(a)/tan(a)
=sin(a).cos(a)/sin(a)/cos(a)....tan.a=sin.a/cos.a
:.sin(a)×sin(a).....cos cancelled out
=sin.sq.(a)