If ϕ1 and ϕ2 be the angles of dip observed in two vertical planes at right angles to each other and ϕ be the true angle of dip, then
cos2ϕ=cos2ϕ1+cos2ϕ2
sec2ϕ=sec2ϕ1+sec2ϕ2
tan2ϕ=tan2ϕ1+tan2ϕ2
cot2ϕ=cot2ϕ1+cot2ϕ2
tan ϕ1=tan ϕcos θ ; cos θ=tan ϕtan ϕ1cos90-θ=sin θ=tan ϕtan ϕ2sin2 θ+cos2 θ=1=tan2 ϕcot2 ϕ1+cot2 ϕ2cot2 ϕ=cot2 ϕ1+cot2 ϕ2