Question

secx-cosx=(tanx)(sinx) prove it

Answer 1

If we so desire, we can also modify the right-hand side to match the left-hand side.

We should write sinxtanx in terms of sinx and cosx, using the identity tanx=sinxcosx:

sinxtanx=sinx(sinxcosx)=sin2xcosx

Now, we use the Pythagorean identity, which is sin2x+cos2x=1. We can modify this to solve for sin2x, so: sin2x=1−cos2x:

sin2xcosx=1−cos2xcosx

Now, just split up the numerator:

1−cos2xcosx=1cosx−cos2xcosx=1cosx−cosx

Use the reciprocal identity secx=1cosx:

1cosx−cosx=secx−cosx

Answer 2

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