If `cos4x=a_0+a_1cos^2x+a^2cos^4x`is true for all values of `x in R ,` – InterviewSolution

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1.	If `cos4x=a_0+a_1cos^2x+a^2cos^4x`is true for all values of `x in R ,`then the value of `5a_0+a_1+a_2`is_______
Answer» Correct Answer - 5 `cos 4x=2 cos^(2) 2x-1` `=2(2 cos^(2) x-1)^(2)-1` `=2(4 cos^(4) x+1-4 cos^(2) x)-1` `=8 cos^(4) x-8 cos^(2) x+1` `:. a_(0)=1, a_(1)=-8, a_(2)=8` `:. 5a_(0)+a_(1)+a_(2)=5`

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