csc^4 x − 2csc^2 x + 1 = cot^4 x
(1/sin x)^4 − 2(1/sin x)^2 + 1 = (cos x/sin x)^4
Multiplying by sin^4 x on both sides, we get
1 - 2sin ^2 x + sin^4 x = cos^4 x
1 - 2(1 - cos^2 x) + (1 - cos^2 x)^2 = cos^4 x
1 - 2 - 2cos^2 x + 1 + cos^4 x - 2cos^2 x = cos^4 x
2 - 2 + 2cos^2 x - 2cos^2 x + cos^4 x = cos^4 x
cos^4 x = cos^4 x
By dividing by sin^4 x on both sides, we get
cos^4 x / sin^4 x = cos^4 x / sin^4 x
cot^4 x = cot^4 x
L.H.S = R.H.S
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