Show that for all such that .

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Show that lim⁡h→0tan⁡(x+h)−tan⁡xh=sec⁡2x\displaystyle \lim_{h\to 0}\frac{\tan(x+h)-\tan x}{h}=\sec^{2}x for all xx such that cos⁡x≠0\cos x\neq 0.

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