How do i solve sinx/cosx(sinx+cosx/sinx×cosx)=secx?

I know it's 1/cosx because it equals secx but I don't know how to get there? :^(

3 answers

try tossing in some parentheses to make it clear just what is in the denominators...
I still don't get it?
sinx/cosx(sinx+cosx/sinx×cosx)
As written, it's

sinx/cosx (sinx + (cosx/sinx) * cosx)
which I doubt is what you meant. I expect you wanted

(sinx/cosx)*((sinx+cosx)/(sinx*cosx))
= sec^2x (sinx+cosx)
which is not secx.

so, what do you really mean?
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