f-x-sin-x-n-cos-x-n-if-f-x-1-n-

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

f (x) = \frac{\sin (x + n)}{\cos (x - n)}

if f (x) = 1, n = ? ?

Commented by arge last updated on 03/Feb/17

o j o c o n l a s i d e n t i d a d e s y d e r i v a d a s . S a l u 2 .

Answered by mrW1 last updated on 31/Jan/17

a n o t h e r w a y :

\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

\Rightarrow n = \frac{π}{4} + i π, i \in Z

Answered by arge last updated on 03/Feb/17

f^{'} (x) = c o s (2 n) {s e c}^{2} (n - x) = m

f^{'} (x) = 0

0 = c o s (2 n) {s e c}^{2} (n - x)

c o s (2 n) = 0

2 n = {c o s}^{- 1} 0

2 n = 90^{°}

n = 45^{°}

c o m p r o b a c i o n :

0 = c o s 90 ° {s e c}^{2} (90 ° - x)

0 = 0

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