L f(t) = cos^4t

Asked by Yash | 9th Jan, 2022, 06:10: PM

Expert Answer:

TO find: L f(t) = cos4t
straight L left parenthesis straight f left parenthesis straight t right parenthesis right parenthesis space equals space straight L left parenthesis cos to the power of 4 straight t right parenthesis
equals straight L left parenthesis left parenthesis cos squared straight t right parenthesis squared right parenthesis space equals straight L open square brackets open parentheses fraction numerator 1 plus cos 2 straight t over denominator 2 end fraction close parentheses squared close square brackets
equals 1 fourth straight L open parentheses 1 plus 2 cos 2 straight t plus cos squared 2 straight t close parentheses
equals 1 fourth straight L open parentheses fraction numerator 2 plus 4 cos 2 straight t plus 1 plus cos 4 straight t over denominator 2 end fraction close parentheses
equals 1 over 8 straight L open parentheses 3 plus 4 cos 2 straight t plus cos 4 straight t close parentheses
equals 1 over 8 open square brackets straight L open parentheses 3 close parentheses plus 4 straight L open parentheses cos 2 straight t close parentheses plus straight L open parentheses cos 4 straight t close parentheses close square brackets
equals fraction numerator 3 over denominator 8 straight S end fraction plus fraction numerator 4 straight S over denominator 8 open parentheses straight S squared plus 4 close parentheses end fraction plus fraction numerator straight S over denominator 8 open parentheses straight S squared plus 16 close parentheses end fraction
 

Answered by Renu Varma | 16th Jan, 2022, 02:00: PM

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