Question

prove d(sinx)/dx=cosx

Answer 1

We know Sin 2x - Sin 2y = 2 cos(x+y) sin(x-y) 

So it follows that sin(x+h) - sin(x) = 2 cos(x+h/2) sin(h/2)

If you divide both sides by h, and take the limit as h approaches zero, you get

d/dx (sin x) = cos(x) limh−>0 sin(h/2)/(h/2)

That limit is 1, of course so the result follows.


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