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Q.

The plane of the dip circle is set in the geographical meridian and apparent dip is θ1. It is then set in a vertical plane perpendicular to the geographical meridian, the apparent dip becomes θ2. The angle of declination α at that place is given by

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a

tan ⁡α=tan ⁡θ1tan ⁡θ2

b

tan⁡ α=tan2 ⁡θ1+tan2 ⁡θ2

c

tan⁡ α=tan ⁡θ1tan ⁡θ2

d

tan⁡ α=tan⁡ θ2tan⁡ θ1

answer is C.

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Detailed Solution

tan⁡ θ1=tan ⁡θcos ⁡α and d tan ⁡θ2=tan ⁡θcos⁡ 90∘−α=tan ⁡θsin⁡ α⇒cos⁡ α=tan⁡ θtan⁡ θ1                    .....(1)and             sin⁡ α=tan ⁡θtan⁡ θ2       ....(2)Dividing (2) by (1), we havetan ⁡α=tan⁡ θ1tan⁡ θ2.
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