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Calculus/identity
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Question
I was wondering could u show me how to idetify this identity:
cosx+sinx*tanx=secx
I convert most everything in trig to sinx and cosx.
I know that tanx = sinx/cosx. I also know that secx = 1/cosx.
Now the right side is 1/cosx.
It is known that 1 =sin^2x + cos^2x, or cos^2x + sin^2x.
Putting this in and splitting the fraction apart as we do it,
we have cos^2x/cosx + sin^2x/cosx.
In the first fraction, the cosx/cosx cancels out.
Since the top is cos^2x,
cancelling one out means now that it is just cosx.
In the second fraction,
note that we can take one of the sinx on top and divide by cosx.
It is known that sinx/cosx = tanx.
We are still left with the other sinx on top,
so this term is sinx*tanx.
All total, I showed that the right side (secx), is equal to
cosx + sinx*tanx.
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