Question Number 114272 by bemath last updated on 18/Sep/20

find solution set of equation   cos 3x = −cos x , x∈(0,3π)

Commented bymalwaan last updated on 18/Sep/20

(i) cos 3x= cos (π−x)  ⇒3x= ±(π−x)+2kπ  (a) 3x=(π−x)+2kπ  ⇒x= π(((1+2k)/4))  (b)3x=−(π−x)+2kπ  ⇒x= π(((2k−1)/2))  (ii) cos 3x= cos(π+x)  ⇒3x= ±(π+x)+2kπ  (a) 3x=(π+x)+2kπ  ⇒x= π(((1+2k)/2))  (b) 3x= −(π+x)+2kπ  ⇒x= π(((2k−1)/4))  ∴ solution set =  {π(((2k±1)/2)) ; π(((2k±1)/4))}

Commented bybemath last updated on 18/Sep/20

hahaha santuy

Commented byabdullahquwatan last updated on 18/Sep/20

kenapa pake santuy sih??

Answered by bemath last updated on 18/Sep/20

Answered by malwaan last updated on 18/Sep/20

x={π(((2k±1)/2)) ; π(((2k±1)/4))}  x∈(0,3)  k=1⇒x= (π/2) ; ((3π)/2) ; (π/4) ; ((3π)/4)(<3π)  k=2⇒x= ((5π)/2) ; ((5π)/4) (<3π)  k= 3⇒x=  ((7π)/4) (<3π)  k= 4 ⇒x= ((9π)/4) (<3π)  k= 5⇒x= ((11π)/4) (3π)

Answered by Dwaipayan Shikari last updated on 18/Sep/20

cos3x+cosx=0  2cos2xcosx=0  cos2x=0  2x=kπ+(π/2)  x=((kπ)/2)+(π/4)  or  x=kπ+(π/2)    (k∈Z)  Solution set  x∈[(π/4),((3π)/4),((5π)/4),((7π)/4),((9π)/4),((11π)/4)]  x∈[(π/2),((3π)/2),((5π)/2)]