Answer
$$\lim_{x\to0}\sec\Big[e^x+\pi\tan\Big(\frac{\pi}{4\sec x}\Big)-1\Big]=-1$$
Work Step by Step
$$A=\lim_{x\to0}\sec\Big[e^x+\pi\tan\Big(\frac{\pi}{4\sec x}\Big)-1\Big]$$
$$A=\lim_{x\to0}\sec\Big[e^x+\pi\tan\Big(\frac{\pi\cos x}{4}\Big)-1\Big]$$
$$A=\sec\Big[e^0+\pi\tan\Big(\frac{\pi\cos0}{4}\Big)-1\Big]$$
$$A=\sec\Big[1+\pi\tan\Big(\frac{\pi}{4}\Big)-1\Big]$$
$$A=\sec\Big[\pi\times1\Big]$$
$$A=\sec\pi=\frac{1}{\cos\pi}=\frac{1}{-1}=-1$$
