f(x) = (10cosx+5cos3x+cos5x)/cos6x+6cos4x+15cos2x+10.
in this expression cosx=t
cos3x=4cos3x-3cosx = 4t3-3t
cos5x=cos(3x+2x) = cos3xcos2x - sin3xsin2x
= (4cos3x-3cosx)(2cos2x-1) - (3sinx-4sin3x)(2sinxcosx)
= (4t3-3t)(2t2-1 ) - (6sin2xcosx-8sin4xcosx)
= (8t5-6t3-4t3+3t) - (6(1-cos2x)cosx - 8(1-cos2x)2cosx)
= ( 8t5-6t3-4t3+3t) - (6(1-t2)t - 8(1-t2)2t) = open this
similarly for cos2x = 2cos2x-1 = 2t2-1
cos4x = 2cos22x -1 = 2 (2t2-1)2 -1
cos6x=2cos23x-1 =2(4t3-3x)2
than put value in f(x)
we will get f(x) =16t5/32t6 = 1/2t =1/2cosx
Moderation Team
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