Question

Demostrar la siguiente identidad: 1/sec²θ=sen²θ . cos²θ+cos⁴θ

Answer 1

${\sin^2x.\cos ^2x+\cos^4x=}\\\\{(1-\cos^2x).\cos^2x+\cos^4x=}\\\\{\cos^2x-\cos^4x+\cos^4x=}\\\\{\cos^2x=}\\\\\\{\boxed{\boxed{\dfrac{1}{\sec^2x}}}}$