M2 Trigonometry (2)

1.
(a) Prove sinθ/(1-cosθ) -cotθ =cscθ.
(b) Hence or otherwise, simply {sin²(-θ) / [cos(θ+180°)+1]} +tan(θ+270°)cos(90°-θ)-cos²(720°+θ), where θ is measured in degree

2. Given that cos(45°-θ) is the repeated root of the equation 5x² +2√(15)x +k=0,
(a) find k.
(b) hence or otherwise, evaluate sin(45°-θ) +cot²(45°+θ).