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)]