Sin2x+sin4x+sin6x=0

Asked by Chirag | 2nd Jan, 2018, 12:34: PM

Expert Answer:

begin mathsize 16px style sin space 2 straight x plus sin space 4 straight x plus sin space 6 straight x equals 0
rightwards double arrow sin space 4 straight x plus left parenthesis sin space 2 straight x plus sin space 6 straight x right parenthesis equals 0
rightwards double arrow sin space 4 straight x plus 2 space sin space 4 straight x space cos space 2 straight x equals 0
rightwards double arrow sin space 4 straight x left parenthesis 1 plus 2 cos space 2 straight x right parenthesis equals 0
rightwards double arrow sin space 4 straight x equals 0 space or space 1 plus 2 cos space 2 straight x equals 0
rightwards double arrow sin space 4 straight x equals 0 space or space cos space 2 straight x equals negative 1 half
Now comma space
sin space 4 straight x equals 0
rightwards double arrow 4 straight x equals nπ comma space straight n element of straight z rightwards double arrow straight x equals nπ over 4 comma space straight n element of straight Z
cos space 2 straight x equals negative 1 half
rightwards double arrow cos space 2 straight x equals cos fraction numerator 2 straight pi over denominator 3 end fraction
rightwards double arrow 2 straight x equals 2 mπ plus-or-minus fraction numerator 2 straight pi over denominator 3 end fraction comma space straight m element of straight Z
rightwards double arrow straight x equals mπ plus-or-minus straight pi over 3 comma space straight m element of straight Z
rightwards double arrow straight x equals nπ over 4 space or space straight x equals mπ plus-or-minus straight pi over 3 comma space where space straight m comma space straight n element of straight Z end style

Answered by Rashmi Khot | 5th Jan, 2018, 11:11: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.