Question

How do you prove `csc ^4theta -2csc ^2 theta +1 = cot^4 theta`?

Answer 1

Prove trig expression.

Explanation:

`csc^4 x - 2csc^2 x + 1 = 1/sin^4 x - 2/sin^2 x + sin^4 x/sin^4 x =`
`= (1 - 2sin^2 x - sin^4 x)/(sin^4 x) = (1 - sin^2 x)^2/sin^4 x =`
`= cos^4 x/sin^4 x = cot^4 x`