Question

Question #8154d

Answer 1

Use the identities `sin2x = 2sinxcosx` and `cos2x = cos^2x - sin^2x`.

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

`2cosx - (cos^2x - sin^2x)/cosx = 1/cosx`

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

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

Now use `sin^2x + cos^2x =1`.

`1/cosx = 1/cosx`

The identity has been proved.

Practice exercises:

`1`. Is the following identity true or false?

`(cos2x)/(cosx + sinx)^2 = 1/(cosx - sinx)`

Solution

`1`. False

Hopefully this helps, and good luck!