proving trig identities: csc^4 - cot^4 = csc^2 + cot^2

[891006]

I need help with one or both:

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

2) (1 - tan^2) / (1 + tan^2) = 1 - 2sin^2

Thanks!!

 

[jwpaine]

Please show any and all work thus far.

Thanks,
John

 

[Deleted member 4993]

Re: proving trig identities

i need help with one or both:

csc^4 - cot^4 = csc^2 + cot^2

Hints:

Use

a^2 - b^2 = (a+b)(a-b)

and

1 + cot^2(x) = cosec^2(x)


(1 - tan^2) / (1 + tan^2) = 1 - 2sin^2

Hints:

1 + tan^2(x) = sec^2(x)

Thanks!!