Question

1. Factor and simplify: cos² xcsc² x-cos²xcot² x

Answer 1

Cos² x

Explanation:

Trigonometry:

`\sf Cos^2 \ x *Csc^2 \ x-Cos^2 \ x *Cot^2 \ x = Cos^2 \ x (Csc^2 \ x - Cot^2 \ x)`

`\sf = Cos^2 \ x \left((1)/(Sin^2 \ x) - (Cos^2 \ x)/(Sin^2 \ x)\right)\\\\= Cos^2 \ x \left((1-Cos^2 \ x)/(Sin^2 \ x)\right)\\\\\boxed{\bf Indentity: \ 1 - Cos^2 \ x = Sin^2 \ x}\\\\\\= Cos^2 \ x \left((Sin^2 \ x)/(Sin^2 \ x)\right)\\\\= Cos^2 \ x`