cosx/1-sinx + 1-sinx/cosx = 2/cosx

Question

cosx/1-sinx + 1-sinx/cosx = 2/cosx

Answer 1

Are you trying to verify this?

If so,

work down 1 side to see if you can get to the expression on the other side.

So

cos x 1 - sin x

---------- + -------------

1-sin x cos x

Getting a common denominator so you can add fractions:

cos(x) cos(x) + (1-sin(x))(1-sin(x))

---------------------------------------------

(1-sin(x)) cos(x)

FOIL the top right term

cos^2(x) + 1 - 2 sin(x) + sin^2(x)

--------------------------------------------

(1-sin(x)) cos(x)

cos^2(x) + sin^2(x) = 1, so the numerator becomes

1 + 1 - 2sin(x) = 2 - 2 sin(x) = 2(1-sin(x))

Now have

2(1-sin(x))

-------------

(1-sin(x)) cos(x)

The "1-sin(x)"s cancel, and left with

2

-------

cos(x)

which matches the other side. :-)