If sin θ + cos θ = √(3/2), find sin³θ + cos³θ.

Question

G1 Physics · Accepted Answer

Let S=sinθ+cosθ=√(3/2). S²=1+2sinθcosθ gives sinθcosθ=1/4. Now a³+b³=(a+b)³−3ab(a+b)=S(S²−3/4)=S(3/2−3/4)=(3/4)√(3/2).