Cot 4x (sin5x + sin3x)= cot x (sin5x - sin3x)

Asked by Iamanish2003 | 20th May, 2019, 02:12: PM

Expert Answer:

begin mathsize 16px style straight L. straight H. straight S space equals space cot 4 straight x space left parenthesis sin 5 straight x space plus space sin 3 straight x right parenthesis
space space space space space space space space space space equals fraction numerator cos 4 straight x over denominator sin 4 straight x end fraction open square brackets 2 sin open parentheses fraction numerator 5 straight x space plus space 3 straight x over denominator 2 end fraction close parentheses cos open parentheses fraction numerator 5 straight x space minus space 3 straight x over denominator 2 end fraction close parentheses close square brackets space space space... space since space sinA space plus space sinB space equals space 2 sin open parentheses fraction numerator straight A space plus space straight B over denominator 2 end fraction close parentheses cos open parentheses fraction numerator straight A space minus space straight B over denominator 2 end fraction close parentheses
space space space space space space space space space space equals space fraction numerator cos 4 straight x over denominator sin 4 straight x end fraction cross times space 2 sin 4 xcosx
space space space space space space space space space space equals space 2 cos 4 xcosx space space space space space.... space left parenthesis straight i right parenthesis
straight R. straight H. straight S space equals cot space straight x space left parenthesis sin 5 straight x space minus space sin 3 straight x right parenthesis
space space space space space space space space space space equals cosx over sinx open square brackets 2 sin open parentheses fraction numerator 5 straight x space plus space 3 straight x over denominator 2 end fraction close parentheses sin open parentheses fraction numerator 5 straight x space minus space 3 straight x over denominator 2 end fraction close parentheses close square brackets space space space... space since space sinA space minus space sinB space equals space 2 cos open parentheses fraction numerator straight A space plus space straight B over denominator 2 end fraction close parentheses sin open parentheses fraction numerator straight A space minus space straight B over denominator 2 end fraction close parentheses
space space space space space space space space space space equals space cosx over sinx cross times space 2 cos 4 xsinx
space space space space space space space space space space equals 2 cos 4 xcosx space space space space space space.... space left parenthesis ii right parenthesis
From left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space
straight L. straight H. straight S space equals space straight R. straight H. straight S
rightwards double arrow cot 4 straight x left parenthesis sin 5 straight x space plus sin 3 straight x right parenthesis equals space cot space straight x space left parenthesis sin 5 straight x space minus space sin 3 straight x right parenthesis


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Answered by Yasmeen Khan | 20th May, 2019, 02:35: PM