Answer
$y=2x+1$
Work Step by Step
The slope of the tangent can be calculated by taking first derivative of the function
$y=e^{2x}cos\pi x$
$y'=e^{2x}\frac{d}{dx}(cos\pi x)+cos\pi x\frac{d}{dx}(e^{2x})$
$y'=2cos\pi x(e^{2x})-\pi (e^{2x})sin\pi x$
Slope of the tangent at (0,1) is given as follows:
$y'|_{(0,1)}=2$
The equation of tangent at (0, 1) is
$(y-1)=2(x-0)$
Hence, $y=2x+1$