(coty sec^2 y-coty)/(siny tany+cosy)

Answer 1

cot sec^2 - cot
= cot(sec^2-1)
= cot(-tan^2)
= -tan

sin tan + cos
= sin*sin/cos + cos
= (sin^2 + cos^2)/cos
= 1/cos
= sec

so, doing the division, you have
-tan/sec
= -sin/cos * cos
= -sin
= -cos tan^3

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