Question

Question #d1e3c

Answer 1

Put on a common denominator and use the identity `sectheta = 1/costheta`.

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

Use the identity `sin^2theta + cos^2theta = 1`.

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

`(1 + 2sinx + 1)/(cosx + cosxsinx) = 2/cosx`

`(2 + 2sinx)/(cosx + cosxsinx) = 2/cosx`

`(2(1 + sinx))/(cosx(1 + sinx)) = 2/cosx`

`2/cosx = 2/cosx`

Hopefully this helps!