Trig Identity Proving - need help

1. sin^2x.tanx+cos^2x.cotx+2sinx.cosx=tanx+…
2. sinx(1+tanx)+cosx(1+cotx)=(sinx+cosx)/(s…
3. tanx(1-cot^2x)+cotx(1-tan^2x)=0

Here's what I've tried on the first one:

I tried to change everything to tans and cots which pretty much gave me a big mess after I solved it. I'm not even sure if the tangent and cotangent identities work with squares:
LHS = tanx[(cos^2x)/(cot^2x)] +cotx[(sin^2x)/(tan^2x)]+(2cosx)/(cotx)*…

The rest were a mess too when I tried to solve them.

Any help would be appreciated. Thank you

sin^2(x) * tan(x) + cos^2(x) * cot(x) + 2sin(x) * cos(x)

sin^2(x) * (sin(x)/cos(x)) + cos^2(x) * (cos(x)/sin(x)) + 2sin(x) * cos(x)

(sin^3(x)/cos(x)) + (cos^3(x)/sin(x)) + 2sin(x) * cos(x) ====> LCD

(sin^3(x)*sin(x)/cos(x)*sin(x)) + (cos^3(x) * cos(x) /sin(x)*cos(x)) + 2sin(x) * cos(x) * sin(x) * cos(x) / sin(x) * cos(x)

(sin^4(x)/cos(x)sin(x)) + (cos^4(x) /sin(x)cos(x)) + 2sin^2(x) * cos^2(x) / sin(x) * cos(x)

(sin^4(x) + cos^4(x) + 2sin^2(x) * cos^2(x) ) / sin(x) * cos(x)

(sin^4(x) + 2sin^2(x) * cos^2(x) + cos^4(x) ) / sin(x) * cos(x)

(sin^2(x) + cos^2(x))^2 / sin(x) * cos(x)

(1)^2 / sin(x) * cos(x)

[ 1/ (sin(x) * cos(x)) ] <==== we can make it back since 1 = cos^2(x) + sin^2(x)

[ (cos^2(x) + sin^2(x) )/ (sin(x) * cos(x)) ]

[ cos^2(x) / (sin(x) * cos(x)) ] + [ sin^2(x) )/ (sin(x) * cos(x))

[ cos(x) / (sin(x) ] + [ sin(x) )/ cos(x))

cot(x) + tan(x)

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2)

sin(x) * ( 1 + tan(x) ) + cos(x) * ( 1 + cot(x) )

sin(x) * ( 1 + sin(x)/cos(x) ) + cos(x) * ( 1 + cos(x)/sin(x) )

sin(x) * ( cos(x)/cos(x) + sin(x)/cos(x) ) + cos(x) * ( sin(x)/sin(x) + cos(x)/sin(x) )

sin(x) * ( cos(x) + sin(x) ) /cos(x) ) + cos(x) * ( sin(x) + cos(x) ) / sin(x) )

(sin(x)/cos(x)) * ( cos(x) + sin(x) ) + ( cos(x) /sin(x) ) * ( sin(x) + cos(x) )