(cosxcotx/secx+tanx)+(sinx/secx-tanx)

Answer 1

making everything sin and cos, we have

(cos^2/sin)/(1/cos + sin/cos) + sin/(1/cos - sin/cos)
cos^2/sin * cos/(1+sin) + sin*cos/(1-sin)
cos^3/(sin(1+sin)) + sin*cos/(1-sin)
(cos^3(1-sin) + sin^2*cos(1+sin))/(sin(1-sin^2))
(cos^3 - sin*cos^3 + cos*sin^2 + sin^3)/(sin*cos^2)
(cos^2 - sin*cos^2 + sin^2)/(sin*cos)
cot - cos + tan

whew - better double-check