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Question Number 70653 by naka3546 last updated on 06/Oct/19

$$\underset{x\to \frac{\pi }{2}}{\lim }{(\sin x-\cos x)}^{\tan x}=...$$

Commented by kaivan.ahmadi last updated on 06/Oct/19

$${lim}_{x\to \frac{\pi }{2}}(sinx-cosx-1)tanx=$$$${lim}_{x\to \frac{\pi }{2}}({sin}^{2}x-sinx-tanx)=-\mathrm{\infty }$$$$\Rightarrow {lim}_{x\to \frac{\pi }{2}}{(sinx-cosx)}^{tanx}=e^{-\mathrm{\infty }}=0$$

Answered by sadimuhmud 136 last updated on 06/Oct/19

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