All Questions Topic List
Trigonometry Questions
Previous in All Question Next in All Question
Previous in Trigonometry Next in Trigonometry
Question Number 105650 by bemath last updated on 30/Jul/20
cos−1(2x)+cos−1(x)=π6findx
Answered by bramlex last updated on 30/Jul/20
cos−1(2x)=π6−cos−1(x)cos(cos−1(2x))=cos(π6−cos−1(x))2x=32x+12sin(cos−1(x))4x=3x+sin(cos−1(x))x(4−3)=sin(cos−1(x))x(4−3)=1−cos2(cos−1(x))x(4−3)=1−x2x2(4−3)2=1−x2x2(19−83+1)=1x2=120−83=14(5−23)x=±125−23.▴
Answered by mathmax by abdo last updated on 31/Jul/20
⇒cos(arcos(2x)+cosx)=32⇒2x.x−sin(arcos(2x))sin(cosx)=32⇒2x2−1−(2x)2×1−x2=32⇒(2x2−32)=1−4x2×1−x2⇒(2x2−32)2=(1−4x2)(1−x2)⇒4x4−23x2+34=1−x2−4x2+4x4⇒−23x2+34=1−5x2⇒−83x2+3=4−20x2⇒(20−83)x2=−3⇒(83−20)x2=3⇒x2=383−20⇒x=+−383−20
Terms of Service
Privacy Policy
Contact: info@tinkutara.com