1)cos^2-sin^2 x=1-2 sin^2x

2)1/1-coax+1/1+cos x=2csc^2x

3)(cot ^2x+1)(sin^2x-1)=-cot^2x

I gave you same hints on how to approach identities like these here:

https://www.askmehelpdesk.com/mathematics/verifying-identities-trig-734254.html#post3397050

Please show us your attempt at solving these and we'll help if you get stuck.