Hey guys so I got a couple problems that I am stuck on and hoping to get some help

1.)( cot^2(x)-1)/(1+cot^x(x))=1-2sin^2(x) SOLVED

2.) sin^4(x)-cos^4(x)=2sin^2(x)-1 SOLVED

3.)tan^2(x)sin^2(x)=tan^2(x)+cos^2(x)-1 WORKING ON SEE BOTTOM POST 1

4.) ((sec(x)-tan(x))^2)/(sec(x)csc(x)-tan(x)csc(x))=2tan(x) WORKING ON SEE POST 2

5.) (csc(x)+cot(x))/(tan(x)+sin(x))=cot(x)csc(x) WORKING ON SEE POST 3

6.) sec^4(x)-sec^2(x)=tan^4(x)+tan^2(x) SOLVED

7.) (1+sin(x)+cos(x))^2=2(1+sin(x))(1+cos(x)) SOLVED

For some reason these were the only ones that stumped me however I will keep trying to chug em away while I wait for some help! Thanks guys