how do u solve these math questions?

Question

Verify.
1.(sin5x+sin3x)/(cos3x-cos5x)=cotx
2.cos(x+y)cos(x-y)=1-sin square x-sin square y
3.sec square x-2secxtanx+tan square x= (1-sinx)/(1+sinx)

Answer 1

1.(sin5x+sin3x)/(cos3x-cos5x)=(sin4x * cos2x) /(sin2x * sin4x)
= cotg 2x
2..cos(x+y)cos(x-y)=1-sin square x-sin square y
<=> 2cos(x+y)cos(x-y)=2-2sin square x-2sin square y
<=> cos 2x + cos 2y = cos2x + cos2y ( it is a true statement)

3. I haven't learned about sec so I can't do it, sorry