Question #8154d

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Answer 1 · 2017-03-30T15:58:55

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!