Prove that :

$\dfrac{\text{cos(90° - θ) cos θ}}{\text{cot θ}}$ = 1 - cos² θ

By formula,

cos (90° - θ) = sin θ.

Solving L.H.S. of the equation

$\Rightarrow \dfrac{\text{cos(90° - θ) cos θ}}{\text{cot θ}} \\[1em] \Rightarrow \dfrac{\text{sin θ cos θ}}{\dfrac{\text{cos θ}}{\text{sin θ}}} \\[1em] \Rightarrow \text{sin}^2 θ \\[1em] \Rightarrow \text{1 - cos}^2 θ.$

Since, L.H.S. = R.H.S.

Hence, proved that $\dfrac{\text{cos(90° - θ) cos θ}}{\text{cot θ}}$ = 1 - cos² θ.