Simplifying Trig Identities

1. The problem statement, all variables and given/known data



The length of the curve r(t) = cos^3(t)j+sin^3(t)k, 0 =< t <= pi/2

is



2. Relevant equations



AL in polar = ∫sqrt(r^2 + [dr/dθ]^2)



3. The attempt at a solution



I am having trouble simplifying the terms within the square root. What method should I use to deal with the pieces?



r^2 = (cos^3(t))^2 + 2 cost^3(t)sin^3(t) + (sin^3(t))^2



dr/dθ = 3(cos(t)^2)sin(t) + 3(sin(t)^2)cos(t)



[dr/dθ]^2 = 9[cos^4(t)sin^2(t) + 2cos^3(t)sin^3(t) + sin^4(t)cos^2(t))



sqrt(cos^3(t))^2 + 2 cost^3(t)sin^3(t) + (sin^3(t))^2 + 9[cos^4(t)sin^2(t) + 2cos^3(t)sin^3(t) + sin^4(t)cos^2(t))



Simplified a bit:



sqrt(1 + 4cos^3(t)sin^3(t) + 9 cos^4(t)sin^4(t) +9sin^4(t)cos^2(t))



How would I further simplify from this?