Q. Solve; 3-2cosx-4sinx-cos2x+sin2x=0.

Asked by Balbir | 1st Feb, 2017, 06:27: PM

Expert Answer:

begin mathsize 16px style The space given space equation space is space colon
3 minus space 2 cosx space minus space 4 space sinx space minus cos 2 straight x space plus space sin 2 straight x space equals space 0
rightwards double arrow 3 minus cos 2 straight x space plus space sin 2 straight x space minus space 4 space sinx space minus space 2 cosx space equals space 0
rightwards double arrow 3 minus left parenthesis 1 minus 2 sin squared space straight x right parenthesis plus space 2 space sin space straight x space cos space straight x space minus space 4 space sinx space minus space 2 space cosx space equals space 0
rightwards double arrow 2 space sin squared space straight x space plus space 2 space minus space 4 space sinx plus space 2 space cos space straight x space left parenthesis sin space straight x space minus space 1 right parenthesis equals space 0
rightwards double arrow 2 space left parenthesis sin squared space straight x minus space 2 space sinx plus 1 right parenthesis plus space 2 space cos space straight x space left parenthesis sin space straight x space minus space 1 right parenthesis equals space 0
rightwards double arrow 2 space left parenthesis sin space straight x minus 1 right parenthesis squared plus space 2 space cos space straight x space left parenthesis sin space straight x space minus space 1 right parenthesis equals space 0
rightwards double arrow 2 space left square bracket left parenthesis sin space straight x minus 1 right parenthesis squared space plus cos space straight x space left parenthesis sin space straight x space minus space 1 right parenthesis right square bracket space equals space 0
rightwards double arrow 2 space left parenthesis sin space straight x space minus space 1 right parenthesis left parenthesis sin space straight x minus 1 plus cos space straight x space right parenthesis equals space 0
rightwards double arrow sin space straight x space minus space 1 equals 0 space space space space and space space space space sin space straight x minus 1 plus cos space straight x space equals space 0
rightwards double arrow sin space straight x space equals space 1 space and space sin space straight x plus cos space straight x space equals 1
rightwards double arrow sin space straight x space equals space sin space open parentheses straight pi over 2 close parentheses space and space cos space open parentheses straight x minus straight pi over 4 close parentheses space equals cos space open parentheses straight pi over 4 close parentheses
rightwards double arrow straight x equals nπ plus left parenthesis negative 1 right parenthesis to the power of straight n open parentheses straight pi over 2 close parentheses space space space and space space straight x minus straight pi over 4 equals 2 nπ plus-or-minus straight pi over 4
rightwards double arrow straight x equals nπ plus left parenthesis negative 1 right parenthesis to the power of straight n open parentheses straight pi over 2 close parentheses space space space and space space straight x equals 2 nπ plus-or-minus straight pi over 2 semicolon space straight x space equals space 2 nπ end style
 
 
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Answered by Rebecca Fernandes | 2nd Feb, 2017, 08:11: AM