find-the-general-solution-of-sin4x-cos2x-0-

Question Number 73538 by Rio Michael last updated on 13/Nov/19

f i n d t h e g e n e r a l s o l u t i o n o f

s i n 4 x + c o s 2 x = 0

Answered by ajfour last updated on 13/Nov/19

\cos 2 x (2 \sin 2 x + 1) = 0

\Rightarrow 2 x = (2 n + 1) \frac{π}{2} o r

2 x = (4 n - 1) \frac{π}{2} \pm \frac{π}{3} .

Commented by Rio Michael last updated on 13/Nov/19

t h a n k s s i r

Answered by malwaan last updated on 14/Nov/19

2 s i n 2 x c o s 2 x + c o s 2 x = 0

c o s 2 x (2 s i n 2 x + 1) = 0

c o s 2 x = 0 \Rightarrow 2 x = \frac{π}{2} + 2 n π

\Rightarrow x = \frac{π}{4} + n π

o r 2 s i n 2 x + 1 = 0

\Rightarrow 2 s i n 2 x = - 1 \Rightarrow s i n 2 x = - \frac{1}{2}

\Rightarrow 2 x = (\frac{π}{6} + π) + 2 n π = \frac{7 π}{6} + 2 n π

\Rightarrow x = \frac{7 π}{12} + n π

o r 2 x = (2 π - \frac{π}{6}) + 2 n π

= \frac{11 π}{6} + 2 n π

\Rightarrow x = \frac{11 π}{12} + n π

\Rightarrow x = {(\frac{π}{4} \lor \frac{7 π}{12} \lor \frac{11 π}{12}) + n π}

Facebook Tweet Pin