Complete the identity: cot(t) (tan (t) - sin (t) cos (t)) =? sin^2 (t) sin (t) tan (t) sec (t) csc (t) tan (t) + 1 Solution cot(t)(tan(t) -sin(t)cos(t)) =(cos(t)/sin(t))((sin(t)/cos(t)) -sin(t)cos(t)) =((cos(t)/sin(t))(sin(t)/cos(t)) - (cos(t)/sin(t))sin(t)cos(t)) =1- cos2(t)..................................................................................[sin2A+cos2A =1 is an identity ] =sin2(t) therefore cot(t)(tan(t) -sin(t)cos(t)) =sin2(t).