Checking dimension analysis

Question

I am trying to check the dimensional analysis of a model I made.

dx=$2cosθ$(x$sin^2$θ+√(($x^2$$sin^4$θ+$hxsinθ$)))

dx is a length so LHS: [L]

h and x are also lengths

From the RHS: $1.1([L].1+√([L]^2.1+[L][L].1)$ which leads to $[L]+(√2)[L]$

Is this dimensional consistent or do the coefficients of both sides need to match?

Answer 1

HINT:

For dimensional consistency, One simply needs to make sure that $[M^aL^bT^cA^d]$ is same at both LHS and RHS. and in your case, It is same. So congrats. You got it right