Question

how do you verify csc^4x - 2csc^2x + 1 = cot^4x?

Answer 1

1-sin^2x=cos^2x
cotx=cosx/sinx
First take LHS
csc^4x - 2csc^2x + 1
=(csc^2x-1)^2
=(1/sin^2x-1)^2
=((1-sin^2x)/sin^2x)^2
=(cos^2x/sin^2x)^2
=(cot^2x)^2
=cot^4x

Answer 2

LHS=RHS
Hence the result

Answer 3

Is that clear @jamroz ?

Answer 4

i don't understand how you got (csc^2x-1)^2? @ajprincess

Answer 5

csc^4x-2csc^2x+1
=csc^4x-csc^2x-csc^2x+1
=csc^2x(csc^2x-1)-1(csc^2x-1)
=(csc^2x-1)(csc^2x-1)
=(csc^2x-1)^2
Is that clear nw?

Answer 6

@jamroz is that clear nw?