Question

Find exact solutions of
$\cos(2x + \sqrt{3 } ) = - \cos(2x)$
for
$0 \leqslant x \leqslant 4\pi$
​

Answer 1

Answer:

Step-by-step explanation:

cos(2x+√3)+cos 2x=0

2 cos (2x+√3+2x)/2 cos (2x+√3-2x)/2=0

or cos(2x+√3/2) cos √3/2=0

or cos (2x+√3/2)=0=cos (2n+1)π/2

or 2x+√3/2=(2n+1)π/2

or x=(2n+1)π/4+√3/4

x=π/4+√3/4=(π+√3)/4,(3π+√3)/4,(5π+√3)4,(7π+√3)/4,(9π+√3)/4,(11π+√3)/4,(13π+√3)/4,(15π+√3)/4

(4π=4×3.14=12.56 nearly)

or