`sin^(10) x+cos^(10)x=29/16 cos^(4) 2x` `rArr ((1- cos 2x)/2)^(5) + ((1+cos 2x)/2)^(5) =29/16 cos^(4) 2x` Let `cos 2x=t`. Then `((1-t)/2)^(5)+((1+t)/2)^(5) =29/16 t^(4)` or `24 t^(4)-10 t^(2) -1=0` or `(2t^(2) -1) (12 t^(2) +1) =0` or `t^(2) =1/2` or `cos^(2) 2x=1/2 =(1/sqrt(2))^(2)=("cos" pi/4)^(2)` or `2x=n pi pm pi/4, n in Z` or `x= (n pi)/2 pm pi/8, n in Z`
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