Proof: Derivative of sin x is cos x

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Though we can use the graph of sin x to guess that the derivative is cos x, the graphing method is not a rigorous proof. Here, we give a proof that the derivative of sinx is cosx. This proof relies on three facts:
• Trig formula for the sum of two angles
• Limit of sinx/x =1 as x goes to 0
• Limit of (cos x -1)/x =0 as x goes to 0

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When I first say the thumbnail, I immediately thought of "Proof is left as an exercise to the reader".

antonaparin
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You said you will prove the sin(x)/x limit using L'Hopitals rule. I hope not as that would be circular!

silver