If θ 1 and θ 2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by

Step-by-step solution

∵   apparent dip angle is given by tan ⁡ θ ' = tan ⁡ θ cos ⁡ α where α is the angle between magnetic meridian and the apparent plane ∴ tan ⁡ θ 1 = tan ⁡ θ cos ⁡ α and tan ⁡ θ 2 = tan ⁡ θ cos ⁡ 90 o - α = tan ⁡ θ sin ⁡ α ⇒ sin 2 ⁡ α + cos 2 ⁡ α = 1 ⇒   cot 2 ⁡ θ 2 + cot 2 ⁡ θ 1 = cot 2 ⁡ θ