Find the value of 'n' using dimensional analsis

this can be solved on the principle of homogenity of dimensional analysis.  which states that  the dimensions of the left hand side of the formula should equal to the dimensional formula of the right hand side of the equation.

now the left hand side of the equation is dimensionless  so the right hand side of the equation must be  dimensionless. further trigonometrical furnctions are dimensionless so the inverse trigonometrical functions  so now we are left with aⁿ , which must be dimensionless, so aⁿ  can only be dimensionless if n=0, so the value of n =0, in order to keep the validy ot the  equation.