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