Can somebody please help me verify:
csc^2x-cos^2x(1+tanx)-sin^2x(1-cotx)=cot^2x

As usual for this type of problem first convert the cosecant, tangent, and cotangent functions to their sine and cosine equivalents, then simplify. Look for opportunities to apply other well-known identities such as sin^2x + cos^2x = 1.

As usual for this type of problem first convert the cosecant, tangent, and cotangent functions to their sine and cosine equivalents, then simplify. Look for opportunities to apply other well-known identities such as sin^2x + cos^2x = 1.

Ive been struggling with it, could you solve it with steps for as an example? Ive got like 6 more like this to do.

Show us your attempt at this and I'll help where you get stuck. How far along do you get using the approach I suggested?