Question Number 10242 by FilupSmith last updated on 31/Jan/17

f(x)=((sin(x+n))/(cos(x−n))) if f(x)=1, n=??

Commented byarge last updated on 03/Feb/17

ojo con las identidades y derivadas. Salu2.

Answered by mrW1 last updated on 31/Jan/17

another way: sin (x+n)=cos (x−n) sin x cos n+cos x sin n=cos x cos n+sin x sin n (sin x−cos x)cos n=(sin x−cos x)sin n tan n=1 ⇒ n=(π/4)+iπ, i∈Z

Answered by arge last updated on 03/Feb/17

f ′(x)=cos(2n)sec^2 (n−x)=m f ′(x)=0 0=cos(2n)sec^2 (n−x) cos(2n)=0 2n=cos^(−1) 0 2n=90^° n=45^° comprobacion: 0=cos90°sec^2 (90°−x) 0=0