Trig help please =)?

Question

I am usually good at math, but these 2 problems are killing me!

Solve the proof:

csc^4x - cot^4x = 2csc^2x - 1

and

cos4x - cos2x

Answer 1

csc^4x-cot^4x
=(csc^2x+cot^2x)(csc^2x-cot^2x)
csc^2x-cot^2x=1
cot^2x=csc^2-1
=(csc^2x+csc^2-1)
=2csc^2x-1

cos4x-cos2x you want to prove equal to what?

Answer 2

1. since (x+y)(x-y0=x^2-y^2 so:left hand side:
=(csc^2x+cot^2x)(csc^2x-cot^2x) .........1)
now ID: cot^2x = csc^2x - 1
or csc^2x - cot^2x = 1
=>1)....becomes:
(csc^2x+cot^2x) = csc^2x + cos^2xcsc^2x
=csc^2x(1+cos^2x)
=csc^2x(1+1-sin^2x)
=csc^2x(2-sin^2x)
=2csc^2x-1
proved

2. cos4x - cos2x
cos4x=cos2(2x)

but what you want to prove?

Answer 3

WHA? I stink at math.