f(x)=ctg x

x0=-π/4

y=f(xo)+f'(xo) (x-xo)

f(xo)=ctg (-π/4)= tg π/4 =1

f'(xo) = - 1/sin² (-π/4)= -1/cos² π/4 = -1/(√2/2)²=-4/2= -2

y=1-2(x+π/4) = 1-2x-π/2