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Yes. The equation can be repaired with a π/4 phase rotation (45°) as follows:

+ → ×

Equivalently, a reduction in scale can achieve the same effect:

+ → ·

Indeed, a reduction in scale ad infinitum will complete the transformation:

+ → → → 

Any of these phase operations, performed in typography space, will convert the incorrect equation into a correct form.
Either:
   cos ϕ = sin ϕ_p sin d₁ + cos ϕ_p cos d₁ × cos C

Or:
   cos ϕ = sin ϕ_p sin d₁ + cos ϕ_p cos d₁ · cos C

Or:
   cos ϕ = sin ϕ_p sin d₁ + cos ϕ_p cos d₁ cos C

All of these variants are valid within the typographic solution space.

Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA