Prove the Trigonometric Identity (tan^2 x + 1)cos 2x = 2 - sec^2 x

Demonstrate the Trigonometric Identity sec(x)/(tan(x) + cot(x)) = sin(x)

Simplify the Trigonometric Expression tan^2(x) sec(x) + sec^3(x)

Demonstrate the Trigonometric Identity cot²(x) + (1/(cos(x) * sec(x))) = csc²(x)

Verify the Trigonometric Identity sec(x) = tan(x) * csc(x)