sin^2(x) + cos^2(x) = 1
cosec(x) = 1/sin(x), so divide by sin^2(x):
1 + cot^2(x) = cosec^2(x)
cot^2(x) = cosec^2(x) - 1
= (cosec(x) - 1)(cosec(x) + 1).
If we multiply top and bottom fraction by (cosec(x) + 1)
(cosec(x) + 1) tan^2(x) / (cosec(x) - 1)(cosec(x) + 1)
= (cosec(x) + 1) tan^2(x) / cot^2(x).
Now tan(x)
=1/cot(x) so tan^2(x)
=1/cot^2(x)
(cosec(x) + 1) tan^2(x) tan^2(x
= (cosec(x) + 1) tan^4(x) .
(cosec(x) + 1) tan^4(x).
