Complete the identity cott tan t sin t cos t sin2 t sin t

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)