Question

How do you verify `sinx + cosx + tanxsinx = secx + cos x tan x`?

Answer 1

Apply the identities `sectheta = 1/costheta` and `tantheta = sintheta/costheta`.

`sinx + cosx + sinx/cosx xx sinx = 1/cosx + sinx/cosx xx cosx`

Put on a common denominator:

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

Recall that `sin^2beta + cos^2beta = 1`:

`(1 + sinx cosx)/cosx = (1 + sinx cosx)/cosx`

Hopefully this helps!