Simplify ((csc^2x)(sin^4x+cos^2x))/(cos^2x) - cos^2x = tan^2x*csc^2x+cot^2x+sin^2x-1

Answer 1

Earlier today I gave a lengthy reply to this question which falls along the same lines as yours:

https://www.jiskha.com/questions/1829098/equation-1-tan-2x-cos-2x-sec-2x-csc-2x-sec-4x-csc-2x-cos-2x-1-equation-2
........

I have a start to yours, and I will let you finish it after perusing the other post:

LS = ((csc^2x)(sin^4x+cos^2x))/(cos^2x) - cos^2x
= (1/sin^2 x)(sin^4 x + cos^2 x)/cos^2 x - cos^2 x
= (sin^2 x + cos^2 x/sin^2 x)/cos^2 x - cos^2 x
= sin^2 x/cos^2 x + 1/sin^2 x - cos^2 x
= tan^2 x + csc^2 x - cos^2 x

RS = tan^2x*csc^2x+cot^2x+sin^2x-1
= sin^2 x/cos^2 x * 1/sin^2 x + cos^2 x/ sin^2 x - 1
= 1/cos^2 x + cos^2 x /sin^2 x - 1
= see what you can from here ....