Menu Close

1-2sin-4x-lt-cos-2-4x-solve-




Question Number 57357 by ANTARES VY last updated on 03/Apr/19
1−2sin(4x)<cos^2 (4x)  solve.
12sin(4x)<cos2(4x)solve.
Commented by bshahid010@gmail.com last updated on 03/Apr/19
1−2sin(4x)<cos^2 (4x)  1−2sin(4x)−cos^2 (4x)<0  1−2sin(4x)−1+sin^2 (4x)<0  sin^2 4x−2sin4x<0  sin4x(sin4x−2)<0  sin4x∈(0,2) so sin4x∈(0,1)  x∈(0,sin1)
12sin(4x)<cos2(4x)12sin(4x)cos2(4x)<012sin(4x)1+sin2(4x)<0sin24x2sin4x<0sin4x(sin4x2)<0sin4x(0,2)sosin4x(0,1)x(0,sin1)
Commented by tanmay.chaudhury50@gmail.com last updated on 03/Apr/19
max value of sinθ=1   so i think    sin4x∈(0,1) but   sin4x∉(0,2)   let other comment...
maxvalueofsinθ=1soithinksin4x(0,1)butsin4x(0,2)letothercomment
Answered by tanmay.chaudhury50@gmail.com last updated on 03/Apr/19
sin4x=a  1−2a<1−a^2   a^2 −2a<0  a(a−2)<0  a≠2       a_(max) =1  1>a>0 is the reauired solution   1>sin4x>0  sin(π/2)>sin4x>sin0  (π/8)>x>0
sin4x=a12a<1a2a22a<0a(a2)<0a2amax=11>a>0isthereauiredsolution1>sin4x>0sinπ2>sin4x>sin0π8>x>0
Commented by ANTARES VY last updated on 03/Apr/19
???
???
Answered by einsteindrmaths@hotmail.fr last updated on 03/Apr/19
cos^2 (4x)=1−sin^2 (4x)====>1−sin(4x)<1−sin^2 (4x)  ==>sin^2 (4x)−sin(4x)<0==>sin(4x)(1−sin(4x))<0==>  sin(4x)>0&1−sin(4x)≠0===>x≠{(π/8)+((kπ)/2)/k∈IZ}∪]((kπ)/(2 ));(((2k+1)π)/4)[
cos2(4x)=1sin2(4x)====>1sin(4x)<1sin2(4x)==>sin2(4x)sin(4x)<0==>sin(4x)(1sin(4x))<0==>sin(4x)>0&1sin(4x)0===>x{π8+kπ2/kIZ}]kπ2;(2k+1)π4[
Answered by mr W last updated on 03/Apr/19
1−2 sin (4x)<1−sin^2  (4x)  sin (4x){sin (4x)−2}<0  since sin (4x)−2<0  ⇒sin (4x)>0  or  ⇒0<sin (4x)≤1  ⇒4x∈(2nπ,2nπ+π)  ⇒x∈(((nπ)/2),((nπ)/2)+(π/4)) with n∈W
12sin(4x)<1sin2(4x)sin(4x){sin(4x)2}<0sincesin(4x)2<0sin(4x)>0or0<sin(4x)14x(2nπ,2nπ+π)x(nπ2,nπ2+π4)withnW

Leave a Reply

Your email address will not be published. Required fields are marked *