A. Let 0 = 2x, then the identity cos 2x = 1-2 sin2 x becomes cos e = 1–2 sin2 (0/2). a. Use this fact and lime 40 n = 1 to prove that lim,40 - 0. b. Using the lim,0 definition of a derivative and the result from part (a), show that * cos T = - sin r. c. use the result from part (a), the equation sin' x + cos x = 1 and the product rule to prove that * sin z = cos r.

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: