Simplify. (cos^4 θ−sin^4 θ)/(sin^2 θ)

$\frac{cos^4 θ−sin^4 θ}{sin^2 θ}$

= \(\frac{( cos²θ - sin²θ ) . ( cos²θ + sin²θ ) }{sin²θ}\)

{ using , cos²θ + sin²θ = 1 }

= \(\frac{( cos²θ - sin²θ ) . 1  }{sin²θ}\)

= \(\frac{( cos²θ  }{sin²θ}\) - \(\frac{( sin²θ  }{sin²θ}\)

= cot²θ - 1