Explanation

Divide by 5: (3/5)sinθ+(4/5)cosθ=1. Since (3/5)²+(4/5)²=1, this is sin(θ+φ)=1 with cosφ=3/5, sinφ=4/5, giving sinθ=3/5, cosθ=4/5. Hence 4tanθ+3cotθ=4(3/4)+3(4/3)=3+4=7, option A.