Question Number 114577 by Khalmohmmad last updated on 19/Sep/20

x=(π/(30))  ((cos14x×cos6x)/(cos4x))=?

Commented bybemath last updated on 19/Sep/20

((cos 20x+cos 8x)/(2cos 4x)) = ((cos ((2π)/3)+cos ((4π)/(15)))/(2cos ((2π)/(15))))  = ((−(1/2)+2cos ^2 (((2π)/(15)))−1)/(2cos ((2π)/(15))))

Commented byMJS_new last updated on 19/Sep/20

we can express this with roots but I haven′t  got the time right now

Commented byMJS_new last updated on 20/Sep/20

I get ((13+7(√5)−(√(390+174(√5))))/8)

Commented bybobhans last updated on 20/Sep/20

how sir?

Commented byMJS_new last updated on 20/Sep/20

(π/(30))=6°  cos 84° = sin 6° =sin (36°−30°)  cos 36° =((1+(√5))/4)  cos 24° =cos (60°−36°)  (or use other sums/differences)  now apply formulas for sin(a±b), cos (a±b)

Answered by 1549442205PVT last updated on 20/Sep/20

f(x)=((cos14x×cos6x)/(cos4x))=((cos20x+cos8x)/(2cos4x))   f((π/(30)))=((cos20x+2cos^2 4x−1)/(2cos4x))  =((cos((2π)/3)+2cos^2 ((2π)/(15))−1)/(2cos((2π)/(15))))=((−(1/2)+2cos^2 24°−1)/(2cos24°))