Question

Tanx/cscx + sinx/tanx

Answer 1

Tan(x) = Sin (x) / Cos (x)

Csc(x) = 1/sin(x)

therefore: [sin(x)/cos(x) ] / [1/sin(x)] + sin(x) / [sin(x)/cos(x)]
but division is just multiplication by reciprocal
= sin(x)/cos(x) . sin(x) + sin(x) . cos(x)/sin(x)
= sin^2(x) / cos(x) + cos(x)
=[sin^2(x) + cos^2(x)] / cos(x) --- since sin^2(x) + cos^2(x) = 1
= 1/cos(x)
= sec(x)