Direction of the first secondary maximum in the Fraunhofer diffraction pattern at a single slit is given by (a is the width of the slit)
asinθ=λ2
acosθ=3λ2
asinθ=λ
asinθ=3λ2
For nth secondary maxima path difference
dsinθ=(2n+1)λ2⇒asinθ=3λ2