F-x-log-sin-x-cos-x-log-sin-2x-find-the-Domain-of-F-D-F-

Question Number 151742 by mnjuly1970 last updated on 22/Aug/21

F (x) := \frac{l o g (s i n (x) + c o s (x))}{l o g (s i n (2 x))}

f i n d t h e D o m a i n o f F \dots

D_{F} = ?

Answered by mindispower last updated on 22/Aug/21

F (x + 2 π) = F (x)

w e c a n s t u d y f i n [0, 2 π [

s i n (2 x) > 0 \Rightarrow x \in] 0, \frac{π}{2} [

s i n (x) + c o s (x) = \sqrt{2} s i n (x + \frac{π}{4}) > 0 \Rightarrow x \in] - \frac{π}{4}, \frac{3 π}{4} [

D F =] 0, \frac{π}{2} [