Question

How do you prove that `(secx + tanx)/(cosx + cotx) = sinxsec^2x`?

Answer 1

`(1/cosx + sinx/cosx)/(cosx + cosx/sinx) = sinx(1/cos^2x)`

`((1 + sinx)/cosx)/((cosxsinx + cosx)/sinx) = sinx(1/cos^2x)`

`(1 + sinx)/cosx * sinx/(cosxsinx + cosx) = sinx(1/cos^2x)`

`(1 + sinx)/cosx * sinx/(cosx(sinx + 1)) = sinx(1/cos^2x)`

`sinx/cos^2x = sinx/cos^2x`

Hopefully this helps!